有多少个周长为 n 、三边长都是整数的不等边三角形？

王守恩

有多少个周长为n,三边长都是整数的不等边三角形？

0, 0, 0,  0, 0, 0,  0, 0, 1,  0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16,
14, 19, 16, 21, 19, 24, 21, 27, 24, 30, 27, 33, 30, 37, 33, 40, 37, 44, 40, 48, 44, 52, 48,
56, 52, 61, 56, 65, 61, 70, 65, 75, 70, 80, 75, 85, 80, 91, 85, 96, 91, 102, 96, 108, 102,
114, 108, 120, 114, 127, 120, 133, 127,140, 133, 147, 140, 154,147, 161, 154, 169,....

a(n)=[\(\frac{(n-3GCD(n, 2))^2}{48}\)]   [ ]表示四舍五入

有看见过这个通项公式的，麻烦曝一曝光，谢谢！

王守恩

a(1)=0
a(2)=0
a(3)=0
a(4)=0
a(5)=0
a(6)=0
a(7)=0
a(8)=0
a(9)=1:2,3,4,
a(10)=0
a(11)=1:2,4,5,
a(12)=1:3,4,5,
a(13)=2:2,5,6, 3,4,6,
a(14)=1:3,5,6,
a(15)=3:2,6,7, 3,5,7, 4,5,6,
a(16)=2:3,6,7, 4,5,7,
a(17)=4:2,7,8, 3,6,8, 4,5,8, 4,6,7,
a(18)=3:3,7,8, 4,6,8, 5,6,7,
a(19)=5:2,8,9, 3,7,9, 4,6,9, 4,7,8, 5,6,8,
a(20)=4:3,8,9, 4,7,9, 5,6,9, 5,7,8,
a(21)=7:2,9,0, 3,8,0, 4,7,0, 4,8,9, 5,6,0, 5,7,9, 6,7,8,
a(22)=5:3,9,0, 4,8,0, 5,7,0, 5,8,9, 6,7,9,
a(23)=8:2,0,1, 3,9,1, 4,8,1, 4,9,0, 5,7,1, 5,8,0, 6,7,0, 6,8,9,
a(24)=7
a(25)=10
a(26)=8
a(27)=12
a(28)=10
a(29)=14
a(30)=12
a(31)=16
a(32)=14
a(33)=19
a(34)=16
a(35)=21
a(36)=19
a(37)=24
a(38)=21
a(39)=27
a(40)=24
a(41)=
a(42)=
a(43)=
a(44)=
a(45)=
a(46)=
a(47)=
a(48)=
a(49)=
a(50)=

王守恩

第1串数:边长是整数的三角形。
第2串数:边长是不等整数的三角形。
第1串数依次加上1,2,3就变成了第2串数。

a(3)=1:1,1,1,
a(9)=1:2,3,4,

a(05)=1:1,2,2,
a(11)=1:2,4,5,

a(06)=1:2,2,2,
a(12)=1:3,4,5,

a(07)=2:1,3,3, 2,2,3,
a(13)=2:2,5,6, 3,4,6,

a(08)=1:2,3,3,
a(14)=1:3,5,6,

a(09)=3:1,4,4, 2,3,4, 3,3,3,
a(15)=3:2,6,7, 3,5,7, 4,5,6,

a(10)=2:2,4,4, 3,3,4,
a(16)=2:3,6,7, 4,5,7,

a(11)=4:1,5,5, 2,4,5, 3,3,5, 3,4,4,
a(17)=4:2,7,8, 3,6,8, 4,5,8, 4,6,7,

a(12)=3:2,5,5, 3,4,5, 4,4,4,
a(18)=3:3,7,8, 4,6,8, 5,6,7,

a(13)=5:1,6,6, 2,5,6, 3,4,6, 3,5,5, 4,4,5,
a(19)=5:2,8,9, 3,7,9, 4,6,9, 4,7,8, 5,6,8,

a(14)=4:2,6,6, 3,5,6, 4,4,6, 4,5,5,
a(20)=4:3,8,9, 4,7,9, 5,6,9, 5,7,8,

a(15)=7:1,7,7, 2,6,7, 3,5,7, 3,6,6, 4,4,7, 4,5,6, 5,5,5,
a(21)=7:2,9,0, 3,8,0, 4,7,0, 4,8,9, 5,6,0, 5,7,9, 6,7,8,

a(16)=5:2,7,7, 3,6,7, 4,5,7, 4,6,6, 5,5,6,
a(22)=5:3,9,0, 4,8,0, 5,7,0, 5,8,9, 6,7,9,

a(17)=8:1,8,8, 2,7,8, 3,6,8, 3,7,7, 4,4,7, 4,5,8, 4,6,7, 5,6,6,
a(23)=8:2,0,1, 3,9,1, 4,8,1, 4,9,0, 5,7,1, 5,8,0, 6,7,0, 6,8,9,
......

王守恩

第1串数:边长是整数的三角形(固定中间数是n)。
第2串数:边长是不等整数的三角形(固定中间数是n)。
第1串数依次加上1,2,3就变成了第2串数。

a(1)=1:1,1,1,
a(3)=1:2,3,4,

a(2)=3:1,2,2, 2,2,2, 2,2,3,
a(4)=3:2,4,5, 3,4,5, 3,4,6,

a(3)=6:1,3,3, 2,3,3, 2,3,4, 3,3,3, 3,3,4, 3,3,5,
a(5)=6:2,5,6, 3,5,6, 3,5,7, 4,5,6, 4,5,7, 4,5,8,

a(4)=10:1,4,4, 2,4,4, 2,4,5, 3,4,4, 3,4,5, 3,4,6, 4,4,4, 4,4,5, 4,4,6, 4,4,7,
a(6)=10:2,6,7, 3,6,7, 3,6,8, 4,6,7, 4,6,8, 4,6,9, 5,6,7, 5,6,8, 5,6,9, 5,6,0,

a(5)=15:1,5,5, 2,5,5, 2,5,6, 3,5,5, 3,5,6, 3,5,7, 4,5,5, 4,5,6, 4,5,7, 4,5,8, 5,5,5, 5,5,6, 5,5,7, 5,5,8, 5,5,9,
a(7)=15:2,7,8, 3,7,8, 3,7,9, 4,7,8, 4,7,9, 4,7,0, 5,7,8, 5,7,9, 5,7,0, 5,7,1, 6,7,8, 6,7,9, 6,7,0, 6,7,1, 6,7,2,

a(6)=21:
a(8)=21:

a(7)=28:
a(9)=28:

a(08)=36:
a(10)=36:
......

王守恩

第1串数:边长是整数的三角形(固定最大数是n)。
第2串数:边长是不等整数的三角形(固定最大数是n)。
第1串数依次加上1,2,3就变成了第2串数。

a(1)=1:1,1,1,
a(4)=1:2,3,4,

a(2)=2:1,2,2, 2,2,2,
a(5)=2:2,4,5, 3,4,5,

a(3)=4:1,3,3, 2,2,3, 2,3,3, 3,3,3,
a(6)=4:2,5,6, 3,4,6, 3,5,6, 4,5,6,

a(4)=6:1,4,4, 2,3,4, 2,4,4, 3,3,4, 3,4,4, 4,4,4,
a(7)=6:2,6,7, 3,5,7, 3,6,7, 4,5,7, 4,6,7, 5,6,7,

a(5)=9:1,5,5, 2,4,5, 2,5,5, 3,3,5, 3,4,5, 3,5,5, 4,4,5, 4,5,5, 5,5,5,
a(8)=9:2,7,8, 3,6,8, 3,7,8, 4,5,8, 4,6,8, 4,7,8, 5,6,8, 5,7,8, 6,7,8,

a(6)=12:1,6,6, 2,5,6, 2,6,6, 3,4,6, 3,5,6, 3,6,6, 4,4,6, 4,5,6, 4,6,6, 5,5,6, 5,6,6, 6,6,6,
a(9)=12:2,8,9, 3,7,9, 3,8,9, 4,6,9, 4,7,9, 4,8,9, 5,6,9, 5,7,9, 5,8,9, 6,7,9, 6,8,9, 7,8,9,

a(7)=16:1,7,7, 2,6,7, 2,7,7, 3,5,7, 3,6,7, 3,7,7, 4,4,7, 4,5,7, 4,6,7, 4,7,7, 5,5,7, 5,6,7, 5,7,7, 6,6,7, 6,7,7, 7,7,7,
a(0)=16:2,9,0, 3,8,0, 3,9,0, 4,7,0, 4,8,0, 4,9,0, 5,6,0, 5,7,0, 5,8,0, 5,9,0, 6,7,0, 6,8,0, 6,9,0, 7,8,0, 7,9,0, 8,9,0,

a(08)=20:
a(11)=20:

a(09)=25:
a(18)=25:

a(13)=30:
a(19)=30:

a(14)=36:
a(20)=36:
......