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A187162
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T(n,k) = Number of n-step self-avoiding walks on a k X k X k cube summed over all starting positions.
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10
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1, 8, 0, 27, 24, 0, 64, 108, 48, 0, 125, 288, 342, 96, 0, 216, 600, 1056, 1104, 144, 0, 343, 1080, 2370, 3984, 3240, 240, 0, 512, 1764, 4464, 9612, 14256, 9504, 192, 0, 729, 2688, 7518, 18888, 37470, 51504, 25344, 144, 0, 1000, 3888, 11712, 32712, 77184, 148224
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OFFSET
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1,2
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LINKS
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FORMULA
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a(1,k) = k^3
a(2,k) = 6*k^3 - 6*k^2
a(3,k) = 30*k^3 - 60*k^2 + 24*k for k>1
a(4,k) = 150*k^3 - 426*k^2 + 312*k - 48 for k>2
a(5,k) = 726*k^3 - 2640*k^2 + 2688*k - 720 for k>3
a(6,k) = 3534*k^3 - 15366*k^2 + 19536*k - 7056 for k>4
a(7,k) = 16926*k^3 - 85380*k^2 + 128832*k - 57312 for k>5
a(8,k) = 81390*k^3 - 463074*k^2 + 801216*k - 418032 for k>6
a(9,k) = 387966*k^3 - 2452704*k^2 + 4766544*k - 2833872 for k>7
a(10,k) = 1853886*k^3 - 12825630*k^2 + 27515184*k - 18252624 for k>8
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EXAMPLE
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Solution for n=9 3X3X3
0 0 0 9 0 0 8 0 0
0 2 1 6 0 0 7 0 0
0 3 0 5 4 0 0 0 0
Table starts
1 8 27 64 125 216 343 512 729 1000
0 24 108 288 600 1080 1764 2688 3888 5400
0 48 342 1056 2370 4464 7518 11712 17226 24240
0 96 1104 3984 9612 18888 32712 51984 77604 110472
0 144 3240 14256 37470 77184 137754 223536 338886 488160
0 240 9504 51504 148224 320328 588924 975216 1500408 2185704
0 192 25344 177120 568248 1298016 2466510 4175136 6525450 9619008
0 144 67824 608928 2188608 5299056 10416624 18026640 28617228 42676728
0 0 167016 2013360 8227752 21274896 43422072 76964016 124223214 187527168
0 0 414912 6654048 30938640 85654320 181790352 330218544 541990896 828222216
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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