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楼主: luyuanhong

有六个城市,任两个城市间可铺路也可不铺路,要使得六城市两两联通,有几种铺路法?

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发表于 2017-10-3 17:06 | 显示全部楼层
      1=2^0
      1=2^1 - 1×1×1
      4=2^3 - 1×1×2 - 2× 1 × 1
    38=2^6 - 1×4×3 - 2× 1 × 3 -  8× 1×1
  728=2^10-1×38×4 -2× 4 × 6 -  8× 1×4-64×1×1
a(6)=2^15-1×728×5-2×38×10 - 8× 4×10-64×1×5-1024×1×1
a(7)=2^21-1×a(6)×6-2×728×15-8×38×20-64×4×15-1024×1×6-2^15×1×1
a(8)=2^28-1×a(7)×7-2×a(6)×21-8×728×35-64×38×35-1024×4×21-2^15×1×7-2^21×1×1
a(9)=2^36-1×a(8)×8-2×a(7)×28-8×a(6)×56-64×728×70-1024×38×56-2^15×4×28-2^21×1×8-2^28×1×1
 楼主| 发表于 2017-10-3 20:45 | 显示全部楼层
谢谢楼上 王守恩 的解答。我已将帖子转贴到“陆老师的《数学中国》园地”。
发表于 2017-10-11 14:56 | 显示全部楼层
王守恩 发表于 2017-10-3 17:06
1=2^0
      1=2^1 - 1×1×1
      4=2^3 - 1×1×2 - 2× 1 × 1

王守恩您好,想請教一下,你這樣的式子的思路是什麼呢?
我知道應該是用全部減去不合的,但該如何解釋您的式子呢?
謝謝您。
发表于 2017-10-11 19:33 | 显示全部楼层
pgcci7339 发表于 2017-10-11 14:56
王守恩您好,想請教一下,你這樣的式子的思路是什麼呢?
我知道應該是用全部減去不合的,但該如何解釋您 ...

我说不好,也不知道如何转载。《数学研发论坛》里有位kastin先生挺厉害的,有公式,有解释。
发表于 2017-10-13 09:35 | 显示全部楼层
王守恩 发表于 2017-10-11 19:33
我说不好,也不知道如何转载。《数学研发论坛》里有位kastin先生挺厉害的,有公式,有解释。

謝謝您,我已找到了。
发表于 2017-10-30 20:56 | 显示全部楼层
本帖最后由 王守恩 于 2017-10-30 20:59 编辑

我们用C(8)表示8个城市铺路方法的种数;
我们用C(9)表示9个城市铺路方法的种数;
......................
我们用C(50)表示50个城市铺路方法的种数;
............
我们用C(n)表示n个城市铺路方法的种数;
则有:C(n)=2^[n(n-1)÷2] - n×2^[(n-1)(n-2)÷2]

验算。
(2^( 7 ×8 /2 ) - C( 8 ))÷2^( 7 ×6 /2)=8.0522842407226562500000000000000000000000000000000
(2^( 8 ×9 /2 ) - C( 9 ))÷2^( 8 ×7 /2)=9.0270700454711914062500000000000000000000000000000
(2^( 9 ×10/2) - C(10))÷2^( 9 ×8 /2)=10.010022291913628578186035156250000000000000000000
(2^(10×11/2) - C(11))÷2^(10×9 /2)=11.003165525682561565190553665161132812500000000000
(2^(11×12/2) - C(12))÷2^(11×10/2)=12.000958229163146029350173193961381912231445312500
(2^(12×13/2) - C(13))÷2^(12×11/2)=13.000292221763118230559719279426644789054989814758
(2^(13×14/2) - C(14))÷2^(13×12/2)=14.000089903500021390665865707661486005974893487291
(2^(14×15/2) - C(15))÷2^(14×13/2)=15.000027624237456815526968268049272934357846187581
(2^(15×16/2) - C(16))÷2^(15×14/2)=16.000008426410498591863892697229390994352806551532
(2^(16×17/2) - C(17))÷2^(16×15/2)=17.000002546380489822930135128478315746326307243421
(2^(17×18/2) - C(18))÷2^(17×16/2)=18.000000762063060656877205479509226290854441433355
(2^(18×19/2) - C(19))÷2^(18×17/2)=19.000000225944769640879391336758703432659053191222
(2^(19×20/2) - C(20))÷2^(19×18/2)=20.000000066408487168716424114982731720567118671215
(2^(20×21/2) - C(21))÷2^(20×19/2)=21.000000019362030283649772031376525045675082304198
(2^(21×22/2) - C(22))÷2^(21×20/2)=22.000000005603706314883481708873104052095846720529
(2^(22×23/2) - C(23))÷2^(22×21/2)=23.000000001610899509179799931763401812437795918303
(2^(23×24/2) - C(24))÷2^(23×22/2)=24.000000000460231973638512602317262632959155546632
(2^(24×25/2) - C(25))÷2^(24×23/2)=25.000000000130743978300759439055418685760658333874
(2^(25×26/2) - C(26))÷2^(25×24/2)=26.000000000036948830119278463204593046672849068155
(2^(26×27/2) - C(27))÷2^(26×25/2)=27.000000000010391776705278218125212308980371801402
(2^(27×28/2) - C(28))÷2^(27×26/2)=28.000000000002909685510356016509299209245910287411
(2^(28×29/2) - C(29))÷2^(28×27/2)=29.000000000000811352872460011248771509415445718111
(2^(29×30/2) - C(30))÷2^(29×28/2)=30.000000000000225375546026478579635141881170137644
(2^(30×31/2) - C(31))÷2^(30×29/2)=31.000000000000062380695237054151166056982096427097
(2^(31×32/2) - C(32))÷2^(31×30/2)=32.000000000000017208462458960481100398440691460750
(2^(32×33/2) - C(33))÷2^(32×31/2)=33.000000000000004732326435783024509380987882020296
(2^(33×34/2) - C(34))÷2^(33×32/2)=34.000000000000001297573272417383558518730035202939
(2^(34×35/2) - C(35))÷2^(34×33/2)=35.000000000000000354805176806910088941415178353312
(2^(35×36/2) - C(36))÷2^(35×34/2)=36.000000000000000096765046124788299264961071964185
(2^(36×37/2) - C(37))÷2^(36×35/2)=37.000000000000000026325784313265576338557218060634
(2^(37×38/2) - C(38))÷2^(37×36/2)=38.000000000000000007145569986709604233180724014047
(2^(38×39/2) - C(39))÷2^(38×37/2)=39.000000000000000001935258532322193847928474413692
(2^(39×40/2) - C(40))÷2^(39×38/2)=40.000000000000000000523042845774382003951756217029
(2^(40×41/2) - C(41))÷2^(40×39/2)=41.000000000000000000141083925394067755792560125976
(2^(41×42/2) - C(42))÷2^(41×40/2)=42.000000000000000000037984133744602731251004511347
(2^(42×43/2) - C(43))÷2^(42×41/2)=43.000000000000000000010208235941745155297366516995
(2^(43×44/2) - C(44))÷2^(43×42/2)=44.000000000000000000002738795008469457736147767223
(2^(44×45/2) - C(45))÷2^(44×43/2)=45.000000000000000000000733605805800000686550870270
(2^(45×46/2) - C(46))÷2^(45×44/2)=46.000000000000000000000196196901545675943003228562
(2^(46×47/2) - C(47))÷2^(46×45/2)=47.000000000000000000000052393490752924312952882242
(2^(47×48/2) - C(48))÷2^(47×46/2)=48.000000000000000000000013971597534010699175931850
(2^(48×49/2) - C(49))÷2^(48×47/2)=49.000000000000000000000003720697169369325207932003
(2^(49×50/2) - C(50))÷2^(49×48/2)=50.00000000000000000000000098954711951121999446772
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