This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337031 #14 Feb 01 2021 00:17:44 %S A337031 5,17,5,52,21,5,148,89,21,5,400,357,93,21,5,1060,1424,405,93,21,5, %T A337031 2700,5484,1789,409,93,21,5,6720,20960,7705,1849,409,93,21,5,15760, %U A337031 78412,33048,8257,1853,409,93,21,5,36248,292168,139032,37097,8329,1853,409,93,21,5 %N A337031 Table read by antidiagonals: T(h,n) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2h x 2h x 2h where the walk starts at the center of one of the box's faces. %F A337031 For n <= h, T(h,n) = A116904(n). %F A337031 Row 1 = T(1,n) = A337033(n). %F A337031 For n >= (2h+1)^3, T(h,n) = 0 as the walk contains more steps than there are available lattice points in the 2h X 2h X 2h box. %e A337031 T(1,2) = 17. Taking the first step right,left,forward or backward hits the box's edge after which the walks has three directions for the second step, giving 4*3 = 12 walks in all. A first step upward can be followed by a second step in five directions. The total number of 2-step walks is therefore 12+5 = 17. %e A337031 . %e A337031 The table begins: %e A337031 . %e A337031 5 17 52 148 400 1060 2700 6720 15760 36248 77856 163296 312760... %e A337031 5 21 89 357 1424 5484 20960 78412 292168 1072272 3919000 14145220 50832492... %e A337031 5 21 93 405 1789 7705 33048 139032 583256 2422480 10053452 41415564 170419680... %e A337031 5 21 93 409 1849 8257 37097 164533 728808 3194636 13978148 60739156 263711448... %e A337031 5 21 93 409 1853 8329 37877 171117 776065 3496769 15758504 70593984 315942684... %e A337031 5 21 93 409 1853 8333 37961 172165 786089 3577129 16326745 74257917 337994448... %e A337031 5 21 93 409 1853 8333 37965 172261 787445 3591637 16455441 75254865 344977177... %e A337031 5 21 93 409 1853 8333 37965 172265 787553 3593341 16475617 75451269 346633713... %e A337031 5 21 93 409 1853 8333 37965 172265 787557 3593461 16477709 75478437 346921841... %e A337031 5 21 93 409 1853 8333 37965 172265 787557 3593465 16477841 75480957 346957465... %e A337031 5 21 93 409 1853 8333 37965 172265 787557 3593465 16477845 75481101 346960453... %e A337031 5 21 93 409 1853 8333 37965 172265 787557 3593465 16477845 75481105 346960609... %e A337031 5 21 93 409 1853 8333 37965 172265 787557 3593465 16477845 75481105 346960613... %Y A337031 Cf. A116904 (h->infinity), A337033 (h=1), A337023 (start at center of box), A336862 (start at middle of edge), A337035 (start at corner of box), A001412. %K A337031 nonn,walk,tabl %O A337031 1,1 %A A337031 _Scott R. Shannon_, Aug 12 2020