求x+y+z+u+v+m=N的解组数

白新岭 · 发表于 2022-10-26 14:42

11的剩余类 2 3 4 5 6 7 8 9 10
4 6 7 8 9 10 11 12 13 14
5 7 8 9 10 11 12 13 14 15
6 8 9 10 11 12 13 14 15 16
7 9 10 11 12 13 14 15 16 17
8 10 11 12 13 14 15 16 17 18
9 11 12 13 14 15 16 17 18 19
10 12 13 14 15 16 17 18 19 20
11 13 14 15 16 17 18 19 20 21
12 14 15 16 17 18 19 20 21 22
13 15 16 17 18 19 20 21 22 23
14 16 17 18 19 20 21 22 23 24
15 17 18 19 20 21 22 23 24 25
16 18 19 20 21 22 23 24 25 26
17 19 20 21 22 23 24 25 26 27
18 20 21 22 23 24 25 26 27 28
19 21 22 23 24 25 26 27 28 29
20 22 23 24 25 26 27 28 29 30
21 23 24 25 26 27 28 29 30 31
22 24 25 26 27 28 29 30 31 32
23 25 26 27 28 29 30 31 32 33
24 26 27 28 29 30 31 32 33 34
25 27 28 29 30 31 32 33 34 35
26 28 29 30 31 32 33 34 35 36
27 29 30 31 32 33 34 35 36 37
28 30 31 32 33 34 35 36 37 38
29 31 32 33 34 35 36 37 38 39
30 32 33 34 35 36 37 38 39 40
31 33 34 35 36 37 38 39 40 41
32 34 35 36 37 38 39 40 41 42
33 35 36 37 38 39 40 41 42 43
34 36 37 38 39 40 41 42 43 44
35 37 38 39 40 41 42 43 44 45
36 38 39 40 41 42 43 44 45 46
37 39 40 41 42 43 44 45 46 47
38 40 41 42 43 44 45 46 47 48
39 41 42 43 44 45 46 47 48 49
40 42 43 44 45 46 47 48 49 50

统计4/2 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9
4 4 8 12 16 20 24 28 32 36
10 10 20 30 40 50 60 70 80 90
20 20 40 60 80 100 120 140 160 180
35 35 70 105 140 175 210 245 280 315
56 56 112 168 224 280 336 392 448 504
84 84 168 252 336 420 504 588 672 756
120 120 240 360 480 600 720 840 960 1080
165 165 330 495 660 825 990 1155 1320 1485
220 220 440 660 880 1100 1320 1540 1760 1980
282 282 564 846 1128 1410 1692 1974 2256 2538
348 348 696 1044 1392 1740 2088 2436 2784 3132
415 415 830 1245 1660 2075 2490 2905 3320 3735
480 480 960 1440 1920 2400 2880 3360 3840 4320
540 540 1080 1620 2160 2700 3240 3780 4320 4860
592 592 1184 1776 2368 2960 3552 4144 4736 5328
633 633 1266 1899 2532 3165 3798 4431 5064 5697
660 660 1320 1980 2640 3300 3960 4620 5280 5940
670 670 1340 2010 2680 3350 4020 4690 5360 6030
660 660 1320 1980 2640 3300 3960 4620 5280 5940
633 633 1266 1899 2532 3165 3798 4431 5064 5697
592 592 1184 1776 2368 2960 3552 4144 4736 5328
540 540 1080 1620 2160 2700 3240 3780 4320 4860
480 480 960 1440 1920 2400 2880 3360 3840 4320
415 415 830 1245 1660 2075 2490 2905 3320 3735
348 348 696 1044 1392 1740 2088 2436 2784 3132
282 282 564 846 1128 1410 1692 1974 2256 2538
220 220 440 660 880 1100 1320 1540 1760 1980
165 165 330 495 660 825 990 1155 1320 1485
120 120 240 360 480 600 720 840 960 1080
84 84 168 252 336 420 504 588 672 756
56 56 112 168 224 280 336 392 448 504
35 35 70 105 140 175 210 245 280 315
20 20 40 60 80 100 120 140 160 180
10 10 20 30 40 50 60 70 80 90
4 4 8 12 16 20 24 28 32 36
1 1 2 3 4 5 6 7 8 9

11的剩余类统计6
6 1
7 6
8 21
9 56
10 126
11 252
12 462
13 792
14 1287
15 2002
16 2997
17 4332
18 6062
19 8232
20 10872
21 13992
22 17577
23 21582
24 25927
25 30492
26 35127
27 39662
28 43917
29 47712
30 50877
31 53262
32 54747
33 55252
34 54747
35 53262
36 50877
37 47712
38 43917
39 39662
40 35127
41 30492
42 25927
43 21582
44 17577
45 13992
46 10872
47 8232
48 6062
49 4332
50 2997
51 2002
52 1287
53 792
54 462
55 252
56 126
57 56
58 21
59 6
60 1
合计 1000000
第三步

白新岭 · 发表于 2022-10-26 14:45

周期/分值 6 7 8 9 10 11 12
0 6 7 8 9 10 11 12
11 17 18 19 20 21 22 23
22 28 29 30 31 32 33 34
33 39 40 41 42 43 44 45
44 50 51 52 53 54 55 56
55 61 62 63 64 65 66 67
66 72 73 74 75 76 77 78
77 83 84 85 86 87 88 89
88 94 95 96 97 98 99 100
99 105 106 107 108 109 110 111
110 116 117 118 119 120 121 122
121 127 128 129 130 131 132 133
132 138 139 140 141 142 143 144
143 149 150 151 152 153 154 155
154 160 161 162 163 164 165 166
165 171 172 173 174 175 176 177
176 182 183 184 185 186 187 188
187 193 194 195 196 197 198 199
198 204 205 206 207 208 209 210
209 215 216 217 218 219 220 221
220 226 227 228 229 230 231 232
231 237 238 239 240 241 242 243
242 248 249 250 251 252 253 254
253 259 260 261 262 263 264 265
264 270 271 272 273 274 275 276
275 281 282 283 284 285 286 287
286 292 293 294 295 296 297 298
297 303 304 305 306 307 308 309
308 314 315 316 317 318 319 320
319 325 326 327 328 329 330 331
330 336 337 338 339 340 341 342
341 347 348 349 350 351 352 353
352 358 359 360 361 362 363 364
363 369 370 371 372 373 374 375
374 380 381 382 383 384 385 386
385 391 392 393 394 395 396 397
396 402 403 404 405 406 407 408
407 413 414 415 416 417 418 419
418 424 425 426 427 428 429 430
429 435 436 437 438 439 440 441
440 446 447 448 449 450 451 452
451 457 458 459 460 461 462 463
462 468 469 470 471 472 473 474

统计6 1 6 21 56 126 252 462
1 1 6 21 56 126 252 462
6 6 36 126 336 756 1512 2772
21 21 126 441 1176 2646 5292 9702
56 56 336 1176 3136 7056 14112 25872
126 126 756 2646 7056 15876 31752 58212
252 252 1512 5292 14112 31752 63504 116424
462 462 2772 9702 25872 58212 116424 213444
792 792 4752 16632 44352 99792 199584 365904
1281 1281 7686 26901 71736 161406 322812 591822
1966 1966 11796 41286 110096 247716 495432 908292
2877 2877 17262 60417 161112 362502 725004 1329174
4032 4032 24192 84672 225792 508032 1016064 1862784
5432 5432 32592 114072 304192 684432 1368864 2509584
7056 7056 42336 148176 395136 889056 1778112 3259872
8856 8856 53136 185976 495936 1115856 2231712 4091472
10752 10752 64512 225792 602112 1354752 2709504 4967424
12642 12642 75852 265482 707952 1592892 3185784 5840604
14412 14412 86472 302652 807072 1815912 3631824 6658344
15946 15946 95676 334866 892976 2009196 4018392 7367052
17136 17136 102816 359856 959616 2159136 4318272 7916832
17892 17892 107352 375732 1001952 2254392 4508784 8266104
18152 18152 108912 381192 1016512 2287152 4574304 8386224
17892 17892 107352 375732 1001952 2254392 4508784 8266104
17136 17136 102816 359856 959616 2159136 4318272 7916832
15946 15946 95676 334866 892976 2009196 4018392 7367052
14412 14412 86472 302652 807072 1815912 3631824 6658344
12642 12642 75852 265482 707952 1592892 3185784 5840604
10752 10752 64512 225792 602112 1354752 2709504 4967424
8856 8856 53136 185976 495936 1115856 2231712 4091472
7056 7056 42336 148176 395136 889056 1778112 3259872
5432 5432 32592 114072 304192 684432 1368864 2509584
4032 4032 24192 84672 225792 508032 1016064 1862784
2877 2877 17262 60417 161112 362502 725004 1329174
1966 1966 11796 41286 110096 247716 495432 908292
1281 1281 7686 26901 71736 161406 322812 591822
792 792 4752 16632 44352 99792 199584 365904
462 462 2772 9702 25872 58212 116424 213444
252 252 1512 5292 14112 31752 63504 116424
126 126 756 2646 7056 15876 31752 58212
56 56 336 1176 3136 7056 14112 25872
21 21 126 441 1176 2646 5292 9702
6 6 36 126 336 756 1512 2772
1 1 6 21 56 126 252 462

合成值统计6
6 1
7 6
8 21
9 56
10 126
11 252
12 462
13 792
14 1287
15 2002
16 2997
17 4338
18 6098
19 8358
20 11208
21 14748
22 19089
23 24354
24 30679
25 38214
26 47139
27 57644
28 69930
29 84210
30 100710
31 119670
32 141345
33 166006
34 193941
35 225456
36 260856
37 300516
38 344826
39 394192
40 449037
41 509802
42 576947
43 650952
44 732318
45 821568
46 919263
47 1025898
48 1142113
49 1268568
50 1405944
51 1554944
52 1716294
53 1890744
54 2079069
55 2282070
56 2500569
57 2735494
58 2987544
59 3257694
60 3546944
61 3856320
62 4186875
63 4539690
64 4915875
65 5316570
66 5742947
67 6196176
68 6677706
69 7188426
70 7729716
71 8302986
72 8909677
73 9551262
74 10229247
75 10945172
76 11700612
77 12497184
78 13336428
79 14220528
80 15150513
81 16128238
82 17155593
83 18234504
84 19366934
85 20554884
86 21800394
87 23105544
88 24472476
89 25903080
90 27400570
91 28966020
92 30601830
93 32310440
94 34094325
95 35955990
96 37897965
97 39922800
98 42033060
99 44231376
100 46519740
101 48902580
102 51380595
103 53956470
104 56632905
105 59412610
106 62298300
107 65292690
108 68398490
109 71618400
110 74955231
111 78410514
112 81990039
113 85693554
114 89523679
115 93483024
116 97574184
117 101799734
118 106162224
119 110664174
120 115308069
121 120096606
122 125030169
123 130116184
124 135352854
125 140742384
126 146286944
127 151988664
128 157849629
129 163871874
130 170057379
131 176408064
132 182926246
133 189610344
134 196469799
135 203500674
136 210704409
137 218082384
138 225635914
139 233366244
140 241274544
141 249361904
142 257629329
143 266078526
144 274705005
145 283520670
146 292518870
147 301699930
148 311064090
149 320611500
150 330342215
151 340256190
152 350353275
153 360633210
154 371096901
155 381735900
156 392565040
157 403574430
158 414762930
159 426129290
160 437672145
161 449390010
162 461281275
163 473344200
164 485576910
165 497979356
166 510538014
167 523271064
168 536164929
169 549216654
170 562423149
171 575781184
172 589287384
173 602938224
174 616730024
175 630658944
176 644723856
177 658905024
178 673224264
179 687663984
180 702219064
181 716884224
182 731654034
183 746522924
184 761485194
185 776535024
186 791666484
187 806877576
188 822141684
189 837484864
190 852886014
191 868338324
192 883834874
193 899368644
194 914932524
195 930519324
196 946121784
197 961732584
198 977349786
199 992939940
200 1008534030
201 1024108380
202 1039655190
203 1055166600
204 1070634700
205 1086051540
206 1101409140
207 1116699500
208 1131914610
209 1147053516
210 1162076250
211 1177019040
212 1191856680
213 1206581080
214 1221184140
215 1235657760
216 1249993850
217 1264184340
218 1278221190
219 1292096400
220 1305810876
221 1319318784
222 1332661534
223 1345813524
224 1358767074
225 1371514544
226 1384048344
227 1396360944
228 1408444884
229 1420292784
230 1431897354
231 1443262156
232 1454336514
233 1465166604
234 1475727624
235 1486013004
236 1496016264
237 1505731024
238 1515151014
239 1524270084
240 1533082214
241 1541581524
242 1549774926
243 1557608304
244 1565131884
245 1572322884
246 1579176544
247 1585688244
248 1591853514
249 1597668044
250 1603127694
251 1608228504
252 1612966704
253 1617353136
254 1621332000
255 1624956640
256 1628207490
257 1631082300
258 1633579010
259 1635695760
260 1637430900
261 1638783000
262 1639750860
263 1640333520
264 1640546216
265 1640333520
266 1639750860
267 1638783000
268 1637430900
269 1635695760
270 1633579010
271 1631082300
272 1628207490
273 1624956640
274 1621332000
275 1617353136
276 1612966704
277 1608228504
278 1603127694
279 1597668044
280 1591853514
281 1585688244
282 1579176544
283 1572322884
284 1565131884
285 1557608304
286 1549774926
287 1541581524
288 1533082214
289 1524270084
290 1515151014
291 1505731024
292 1496016264
293 1486013004
294 1475727624
295 1465166604
296 1454336514
297 1443262156
298 1431897354
299 1420292784
300 1408444884
301 1396360944
302 1384048344
303 1371514544
304 1358767074
305 1345813524
306 1332661534
307 1319318784
308 1305810876
309 1292096400
310 1278221190
311 1264184340
312 1249993850
313 1235657760
314 1221184140
315 1206581080
316 1191856680
317 1177019040
318 1162076250
319 1147053516
320 1131914610
321 1116699500
322 1101409140
323 1086051540
324 1070634700
325 1055166600
326 1039655190
327 1024108380
328 1008534030
329 992939940
330 977349786
331 961732584
332 946121784
333 930519324
334 914932524
335 899368644
336 883834874
337 868338324
338 852886014
339 837484864
340 822141684
341 806877576
342 791666484
343 776535024
344 761485194
345 746522924
346 731654034
347 716884224
348 702219064
349 687663984
350 673224264
351 658905024
352 644723856
353 630658944
354 616730024
355 602938224
356 589287384
357 575781184
358 562423149
359 549216654
360 536164929
361 523271064
362 510538014
363 497979356
364 485576910
365 473344200
366 461281275
367 449390010
368 437672145
369 426129290
370 414762930
371 403574430
372 392565040
373 381735900
374 371096901
375 360633210
376 350353275
377 340256190
378 330342215
379 320611500
380 311064090
381 301699930
382 292518870
383 283520670
384 274705005
385 266078526
386 257629329
387 249361904
388 241274544
389 233366244
390 225635914
391 218082384
392 210704409
393 203500674
394 196469799
395 189610344
396 182926246
397 176408064
398 170057379
399 163871874
400 157849629
401 151988664
402 146286944
403 140742384
404 135352854
405 130116184
406 125030169
407 120096606
408 115308069
409 110664174
410 106162224
411 101799734
412 97574184
413 93483024
414 89523679
415 85693554
416 81990039
417 78410514
418 74955231
419 71618400
420 68398490
421 65292690
422 62298300
423 59412610
424 56632905
425 53956470
426 51380595
427 48902580
428 46519740
429 44231376
430 42033060
431 39922800
432 37897965
433 35955990
434 34094325
435 32310440
436 30601830
437 28966020
438 27400570
439 25903080
440 24472476
441 23105544
442 21800394
443 20554884
444 19366934
445 18234504
446 17155593
447 16128238
448 15150513
449 14220528
450 13336428
451 12497184
452 11700612
453 10945172
454 10229247
455 9551262
456 8909677
457 8302986
458 7729716
459 7188426
460 6677706
461 6196176
462 5742947
463 5316570
464 4915875
465 4539690
466 4186875
467 3856320
468 3546944
469 3257694
470 2987544
471 2735494
472 2500569
473 2282070
474 2079069
475 1890744
476 1716294
477 1554944
478 1405944
479 1268568
480 1142113
481 1025898
482 919263
483 821568
484 732318
485 650952
486 576947
487 509802
488 449037
489 394192
490 344826
491 300516
492 260856
493 225456
494 193941
495 166006
496 141345
497 119670
498 100710
499 84210
500 69930
501 57644
502 47139
503 38214
504 30679
505 24354
506 19089
507 14748
508 11208
509 8358
510 6098
511 4338
512 2997
513 2002
514 1287
515 792
516 462
517 252
518 126
519 56
520 21
521 6
522 1
合计 262144000000

白新岭 · 发表于 2022-10-26 15:04

模5 1 3 4
1 2 4 5
3 4 6 7
4 5 7 8

5的剩余类统计2
2 1
4 2
5 2
6 1
7 2
8 1
合计 9
第一步

白新岭 · 发表于 2022-10-26 15:04

5的剩余类 2 4 5 6 7 8
2 4 6 7 8 9 10
4 6 8 9 10 11 12
5 7 9 10 11 12 13
6 8 10 11 12 13 14
7 9 11 12 13 14 15
8 10 12 13 14 15 16

统计2 1 2 2 1 2 1
1 1 2 2 1 2 1
2 2 4 4 2 4 2
2 2 4 4 2 4 2
1 1 2 2 1 2 1
2 2 4 4 2 4 2
1 1 2 2 1 2 1

5的剩余类统计4
4 1
6 4
7 4
8 6
9 12
10 10
11 12
12 13
13 8
14 6
15 4
16 1
合计 81
第二步

白新岭 · 发表于 2022-10-26 15:05

5的剩余类 2 4 5 6 7 8
4 6 8 9 10 11 12
6 8 10 11 12 13 14
7 9 11 12 13 14 15
8 10 12 13 14 15 16
9 11 13 14 15 16 17
10 12 14 15 16 17 18
11 13 15 16 17 18 19
12 14 16 17 18 19 20
13 15 17 18 19 20 21
14 16 18 19 20 21 22
15 17 19 20 21 22 23
16 18 20 21 22 23 24

统计4/2 1 2 2 1 2 1
1 1 2 2 1 2 1
4 4 8 8 4 8 4
4 4 8 8 4 8 4
6 6 12 12 6 12 6
12 12 24 24 12 24 12
10 10 20 20 10 20 10
12 12 24 24 12 24 12
13 13 26 26 13 26 13
8 8 16 16 8 16 8
6 6 12 12 6 12 6
4 4 8 8 4 8 4
1 1 2 2 1 2 1

5的剩余类统计6
6 1
8 6
9 6
10 15
11 30
12 35
13 60
14 75
15 80
16 96
17 90
18 76
19 66
20 45
21 26
22 15
23 6
24 1
合计 729
第三步

白新岭 · 发表于 2022-10-26 15:13

周期/分值 6 8 9 10 11 12 13
0 6 8 9 10 11 12 13
5 11 13 14 15 16 17 18
10 16 18 19 20 21 22 23
15 21 23 24 25 26 27 28
20 26 28 29 30 31 32 33
25 31 33 34 35 36 37 38
30 36 38 39 40 41 42 43
35 41 43 44 45 46 47 48
40 46 48 49 50 51 52 53
45 51 53 54 55 56 57 58
50 56 58 59 60 61 62 63
55 61 63 64 65 66 67 68
60 66 68 69 70 71 72 73
65 71 73 74 75 76 77 78
70 76 78 79 80 81 82 83
75 81 83 84 85 86 87 88
80 86 88 89 90 91 92 93
85 91 93 94 95 96 97 98
90 96 98 99 100 101 102 103
95 101 103 104 105 106 107 108
100 106 108 109 110 111 112 113
105 111 113 114 115 116 117 118
110 116 118 119 120 121 122 123
115 121 123 124 125 126 127 128
120 126 128 129 130 131 132 133
125 131 133 134 135 136 137 138
130 136 138 139 140 141 142 143
135 141 143 144 145 146 147 148
140 146 148 149 150 151 152 153
145 151 153 154 155 156 157 158
150 156 158 159 160 161 162 163
155 161 163 164 165 166 167 168
160 166 168 169 170 171 172 173
165 171 173 174 175 176 177 178
170 176 178 179 180 181 182 183
175 181 183 184 185 186 187 188
180 186 188 189 190 191 192 193
185 191 193 194 195 196 197 198
190 196 198 199 200 201 202 203
195 201 203 204 205 206 207 208
200 206 208 209 210 211 212 213
205 211 213 214 215 216 217 218
210 216 218 219 220 221 222 223

统计6 1 6 6 15 30 35 60
1 1 6 6 15 30 35 60
6 6 36 36 90 180 210 360
21 21 126 126 315 630 735 1260
56 56 336 336 840 1680 1960 3360
126 126 756 756 1890 3780 4410 7560
252 252 1512 1512 3780 7560 8820 15120
462 462 2772 2772 6930 13860 16170 27720
792 792 4752 4752 11880 23760 27720 47520
1281 1281 7686 7686 19215 38430 44835 76860
1966 1966 11796 11796 29490 58980 68810 117960
2877 2877 17262 17262 43155 86310 100695 172620
4032 4032 24192 24192 60480 120960 141120 241920
5432 5432 32592 32592 81480 162960 190120 325920
7056 7056 42336 42336 105840 211680 246960 423360
8856 8856 53136 53136 132840 265680 309960 531360
10752 10752 64512 64512 161280 322560 376320 645120
12642 12642 75852 75852 189630 379260 442470 758520
14412 14412 86472 86472 216180 432360 504420 864720
15946 15946 95676 95676 239190 478380 558110 956760
17136 17136 102816 102816 257040 514080 599760 1028160
17892 17892 107352 107352 268380 536760 626220 1073520
18152 18152 108912 108912 272280 544560 635320 1089120
17892 17892 107352 107352 268380 536760 626220 1073520
17136 17136 102816 102816 257040 514080 599760 1028160
15946 15946 95676 95676 239190 478380 558110 956760
14412 14412 86472 86472 216180 432360 504420 864720
12642 12642 75852 75852 189630 379260 442470 758520
10752 10752 64512 64512 161280 322560 376320 645120
8856 8856 53136 53136 132840 265680 309960 531360
7056 7056 42336 42336 105840 211680 246960 423360
5432 5432 32592 32592 81480 162960 190120 325920
4032 4032 24192 24192 60480 120960 141120 241920
2877 2877 17262 17262 43155 86310 100695 172620
1966 1966 11796 11796 29490 58980 68810 117960
1281 1281 7686 7686 19215 38430 44835 76860
792 792 4752 4752 11880 23760 27720 47520
462 462 2772 2772 6930 13860 16170 27720
252 252 1512 1512 3780 7560 8820 15120
126 126 756 756 1890 3780 4410 7560
56 56 336 336 840 1680 1960 3360
21 21 126 126 315 630 735 1260
6 6 36 36 90 180 210 360
1 1 6 6 15 30 35 60

合成值统计6
6 1
8 6
9 6
10 15
11 36
12 35
13 96
14 111
15 170
16 297
17 300
18 562
19 642
20 840
21 1288
22 1290
23 2058
24 2308
25 2790
26 3978
27 3940
28 5748
29 6348
30 7315
31 9954
32 9765
33 13454
34 14679
35 16380
36 21574
37 21000
38 27804
39 30044
40 32760
41 42120
42 40740
43 52380
44 56160
45 60180
46 75945
47 73080
48 91830
49 97830
50 103365
51 128440
52 123045
53 151620
54 160605
55 167610
56 205425
57 195980
58 237330
59 250050
60 258080
61 312384
62 296850
63 353914
64 371004
65 379110
66 453700
67 429540
68 504960
69 526840
70 533505
71 631890
72 596155
73 691950
74 718725
75 721840
76 846840
77 796320
78 913520
79 944880
80 941760
81 1095040
82 1026480
83 1164720
84 1199840
85 1187280
86 1368834
87 1279200
88 1436364
89 1473804
90 1448310
91 1656120
92 1542990
93 1715280
94 1753110
95 1711380
96 1941490
97 1803480
98 1985700
99 2021700
100 1961040
101 2207760
102 2044820
103 2230740
104 2262600
105 2181260
106 2437500
107 2251080
108 2433880
109 2459400
110 2356830
111 2614564
112 2407650
113 2580444
114 2597734
115 2474760
116 2725620
117 2502640
118 2659080
119 2666760
120 2525680
121 2761680
122 2528280
123 2663240
124 2660640
125 2505240
126 2719610
127 2482320
128 2592540
129 2579900
130 2415210
131 2603040
132 2368730
133 2452920
134 2431290
135 2262980
136 2421354
137 2196600
138 2255284
139 2226324
140 2060160
141 2188160
142 1978740
143 2014020
144 1979800
145 1821180
146 1919760
147 1730280
148 1745520
149 1708320
150 1561890
151 1633620
152 1467270
153 1466700
154 1428810
155 1298160
156 1346840
157 1205280
158 1193520
159 1157040
160 1044480
161 1074624
162 958000
163 939504
164 906144
165 812560
166 828765
167 735840
168 714350
169 685230
170 610155
171 616580
172 545055
173 523440
174 499115
175 441090
176 441285
177 388220
178 368490
179 349050
180 305960
181 302760
182 264930
183 248290
184 233460
185 202830
186 198314
187 172500
188 159444
189 148684
190 127935
191 123450
192 106665
193 97110
194 89715
195 76380
196 72630
197 62280
198 55740
199 50940
200 42840
201 40040
202 34020
203 29820
204 26880
205 22260
206 20349
207 17080
208 14574
209 12894
210 10465
211 9288
212 7665
213 6308
214 5433
215 4290
216 3653
217 2940
218 2298
219 1898
220 1440
221 1152
222 890
223 642
224 492
225 350
226 252
227 180
228 112
229 72
230 45
231 26
232 15
233 6
234 1
合计 191102976
40以内数据正确。

王守恩 · 发表于 2022-10-26 19:48

本帖最后由王守恩于 2022-10-27 07:35 编辑

白新岭发表于 2022-10-26 15:13
周期/分值 6 8 9 10 11 12 13
0 6 8 9 10 11 12 13
5 11 13 14 15 16 17 18

57楼答案是错的。说得好:“增加条件，只有变得复杂，不会简单”。

王守恩 · 发表于 2022-10-27 07:15

本帖最后由王守恩于 2022-10-27 07:24 编辑

我们用 f(k,N,M) 来表示

K(1)+K(2)+K(3)+...+K(K-2)+K(K-1)+K(K)=N的解组数，限制条件未知数取数不能取 M 的倍数，

整体通项公式好像搞不出来。还是20楼的公式，虽然M个算式可以合并成1个。

x+y+z+u+v+m=N的解组数，限制条件未知数取数不能取12的倍数

嗨！下面这串数就是一次拖出来的！

0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 252, 462, 792, 1287, 2002, 3003, 4362, 6158, 8478, 11418, 15084, 19593,
25074, 31669, 39534, 48840, 59774, 72555, 87414, 104595, 124356, 146970, 172726, 201930, 234906,
271991, 313566, 359997, 411676, 469062, 532632, 602882, 680328, 765507, 858978, 961323, 1073148,
1195048, 1327788, 1471959, 1628234, 1797399,1980264,2177664,2390460,2619540,2865820,3130245,
3413790, 3717335, 4042290, 4389420, 4759770,5154540,5574960,6022291,6497826,7002891,7538846,
8107086, 8709042, 9345847, 10019982,10732197,11484032,12277188,13113402, 13994448, 14922138,
15898323,16924894,18003783,19136964,20325704,21574224,22882860,24253824,25689405,27191934
28763785,30407376,32125170,33919676,35793450,37749096,39787776,41916456,44134362,46444636
48850242,51354192,53959547,56669418,59486967,62415408,65458008,68618088,71896308,75303828
78837669,82502274,86301369,90238734,94318204,98543670,102919080,107448440,112135815, .......

王守恩 · 发表于 2022-10-27 11:29

我们用 f(k,N,M) 来表示

K(1)+K(2)+K(3)+...+K(K-2)+K(K-1)+K(K)=N的解组数，限制条件未知数取数不能取 M 的倍数，

1,M可以看作就是几块积木(M=5就是11块积木),每块积木的组合数是固定的。

M=1,2,3,4,5,6,7,8,9对应是1, 2, 3, 5, 7, 11, 15, 22, 30块积木

这串数是A000041

a(n)=Table[SeriesCoefficient\(\displaystyle\big[\prod_{j= 1}^n\frac{1}{1-x^j},\big(x, 0, n\big)\big]\),{n,1,28}]

{1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385,
490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718}

2,M=5,K=6,N最小是6。a(6)=1块积木，a(7)=1块积木，a(8)=2块积木，a(9)=3块积木，a(10)=5块积木

这串数是A001402

a(N)=Table[SeriesCoefficient\(\displaystyle\big[\prod_{j= 1}^6\frac{1}{1-x^j},\big(x, 0, n\big)\big]\),{n,0,28}]

{1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 110, 136, 163,
199, 235, 282, 331, 391, 454, 532, 612, 709, 811, 931}

独木星空谁 · 发表于 2022-10-27 14:57

OFFSET
0,3
COMMENTS
Also number of nonnegative solutions to b + 2c + 3d + 4e + ... = n and the number of nonnegative solutions to 2c + 3d + 4e + ... <= n. - Henry Bottomley, Apr 17 2001

a(n) is also the number of conjugacy classes in the symmetric group S_n (and the number of irreducible representations of S_n).

Also the number of rooted trees with n+1 nodes and height at most 2.

Coincides with the sequence of numbers of nilpotent conjugacy classes in the Lie algebras gl(n). A006950, A015128 and this sequence together cover the nilpotent conjugacy classes in the classical A,B,C,D series of Lie algebras. - Alexander Elashvili, Sep 08 2003

Number of distinct Abelian groups of order p^n, where p is prime (the number is independent of p). - Lekraj Beedassy, Oct 16 2004

Number of graphs on n vertices that do not contain P3 as an induced subgraph. - Washington Bomfim, May 10 2005

Numbers of terms to be added when expanding the n-th derivative of 1/f(x). - Thomas Baruchel, Nov 07 2005

Sequence agrees with expansion of Molien series for symmetric group S_n up to the term in x^n. - Maurice D. Craig (towenaar(AT)optusnet.com.au), Oct 30 2006

Also the number of nonnegative integer solutions to x_1 + x_2 + x_3 + ... + x_n = n such that n >= x_1 >= x_2 >= x_3 >= ... >= x_n >= 0, because by letting y_k = x_k - x_(k+1) >= 0 (where 0 < k < n) we get y_1 + 2y_2 + 3y_3 + ... + (n-1)y_(n-1) + nx_n = n. - Werner Grundlingh (wgrundlingh(AT)gmail.com), Mar 14 2007

Let P(z) := Sum_{j>=0} b_j z^j, b_0 != 0. Then 1/P(z) = Sum_{j>=0} c_j z^j, where the c_j must be computed from the infinite triangular system b_0 c_0 = 1, b_0 c_1 + b_1 c_0 = 0 and so on (Cauchy products of the coefficients set to zero). The n-th partition number arises as the number of terms in the numerator of the expression for c_n: The coefficient c_n of the inverted power series is a fraction with b_0^(n+1) in the denominator and in its numerator having a(n) products of n coefficients b_i each. The partitions may be read off from the indices of the b_i. - Peter C. Heinig (algorithms(AT)gmx.de), Apr 09 2007

Equals row sums of triangle A137683. - Gary W. Adamson, Feb 05 2008

a(n) is the number of different ways to run up a staircase with n steps, taking steps of sizes 1, 2, 3, ... and r (r <= n), where the order is not important and there is no restriction on the number or the size of each step taken. - Mohammad K. Azarian, May 21 2008

Equals the eigenvector of triangle A145006 and row sums of the eigentriangle of the partition numbers, A145007. - Gary W. Adamson, Sep 28 2008

Starting with offset 1 = INVERT transform of (1, 1, 0, 0, -1, 0, -1, ...), where A080995, the characteristic function of A001318 (1, 2, 5, 7, 12, ...) is signed (++ -- ++, ...) as to 1's. This is equivalent to lim_{n>=1} A145006^n as a vector. The INVERT transform of (1, 1, 0, 0, -1, ...) begins (1, 2,..) then for each successive operation we take a dot product of (1, 1, 0, 0, -1, ...) in reverse and the ongoing results of our series (1, 2, 3, 5, 7, ...) then add the result to the next term in (1, 1, 0, 0, -1, ...). For example, a (7) = 15 = (0, -1, 0, 0, 1, 1) dot (1, 2, 3, 5, 7, 11) = (0*1, (-1)*2, 0*3, 0*5, 1*7, 1*11) = (-2 + 7 + 11) = 16, then add to (-1) = 15. - Gary W. Adamson, Oct 05 2008

Convolved with A147843 = A000203 prefaced with a zero: (0, 1, 3, 4, 7, ...). - Gary W. Adamson, Nov 15 2008

From Gary W. Adamson, Jun 12 2009: (Start)

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求x+y+z+u+v+m=N的解组数

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