cp's OEIS Frontend

A187162 T(n,k) = Number of n-step self-avoiding walks on a k X k X k cube summed over all starting positions.

%I A187162 #14 Feb 28 2022 07:48:16
%S A187162 1,8,0,27,24,0,64,108,48,0,125,288,342,96,0,216,600,1056,1104,144,0,
%T A187162 343,1080,2370,3984,3240,240,0,512,1764,4464,9612,14256,9504,192,0,
%U A187162 729,2688,7518,18888,37470,51504,25344,144,0,1000,3888,11712,32712,77184,148224
%N A187162 T(n,k) = Number of n-step self-avoiding walks on a k X k X k cube summed over all starting positions.
%H A187162 R. H. Hardin, <a href="/A187162/b187162.txt">Table of n, a(n) for n = 1..241</a>
%F A187162 a(1,k) = k^3
%F A187162 a(2,k) = 6*k^3 - 6*k^2
%F A187162 a(3,k) = 30*k^3 - 60*k^2 + 24*k for k>1
%F A187162 a(4,k) = 150*k^3 - 426*k^2 + 312*k - 48 for k>2
%F A187162 a(5,k) = 726*k^3 - 2640*k^2 + 2688*k - 720 for k>3
%F A187162 a(6,k) = 3534*k^3 - 15366*k^2 + 19536*k - 7056 for k>4
%F A187162 a(7,k) = 16926*k^3 - 85380*k^2 + 128832*k - 57312 for k>5
%F A187162 a(8,k) = 81390*k^3 - 463074*k^2 + 801216*k - 418032 for k>6
%F A187162 a(9,k) = 387966*k^3 - 2452704*k^2 + 4766544*k - 2833872 for k>7
%F A187162 a(10,k) = 1853886*k^3 - 12825630*k^2 + 27515184*k - 18252624 for k>8
%F A187162 ["Empirical" removed by _Andrey Zabolotskiy_, Feb 28 2022]
%e A187162 Solution for n=9 3X3X3
%e A187162   0  0  0     9  0  0     8  0  0
%e A187162   0  2  1     6  0  0     7  0  0
%e A187162   0  3  0     5  4  0     0  0  0
%e A187162 Table starts
%e A187162   1   8     27      64      125      216       343       512       729      1000
%e A187162   0  24    108     288      600     1080      1764      2688      3888      5400
%e A187162   0  48    342    1056     2370     4464      7518     11712     17226     24240
%e A187162   0  96   1104    3984     9612    18888     32712     51984     77604    110472
%e A187162   0 144   3240   14256    37470    77184    137754    223536    338886    488160
%e A187162   0 240   9504   51504   148224   320328    588924    975216   1500408   2185704
%e A187162   0 192  25344  177120   568248  1298016   2466510   4175136   6525450   9619008
%e A187162   0 144  67824  608928  2188608  5299056  10416624  18026640  28617228  42676728
%e A187162   0   0 167016 2013360  8227752 21274896  43422072  76964016 124223214 187527168
%e A187162   0   0 414912 6654048 30938640 85654320 181790352 330218544 541990896 828222216
%Y A187162 Cf. A187163, A187164, A187165, A187166, A187167, A187168, A187169, A187170, A187171.
%K A187162 nonn,tabl
%O A187162 1,2
%A A187162 _R. H. Hardin_, Mar 06 2011