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 A333509 #23 Mar 26 2020 07:11:17 %S A333509 1,1,8,1,16,29,1,32,95,80,1,64,313,426,195,1,128,1033,2320,1745,444,1, %T A333509 256,3411,12706,16347,6838,969,1,512,11265,69662,154259,112572,25897, %U A333509 2056,1,1024,37205,381964,1454495,1859660,752245,95292,4279 %N A333509 Square array T(n,k), n >= 1, k >= 2, read by antidiagonals, where T(n,k) is the number of self-avoiding walks in the n X k grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side. %e A333509 Square array T(n,k) begins: %e A333509 1, 1, 1, 1, 1, ... %e A333509 8, 16, 32, 64, 128, ... %e A333509 29, 95, 313, 1033, 3411, ... %e A333509 80, 426, 2320, 12706, 69662, ... %e A333509 195, 1745, 16347, 154259, 1454495, ... %e A333509 444, 6838, 112572, 1859660, 30549774, ... %o A333509 (Python) %o A333509 # Using graphillion %o A333509 from graphillion import GraphSet %o A333509 import graphillion.tutorial as tl %o A333509 def A(start, goal, n, k): %o A333509 universe = tl.grid(n - 1, k - 1) %o A333509 GraphSet.set_universe(universe) %o A333509 paths = GraphSet.paths(start, goal) %o A333509 return paths.len() %o A333509 def A333509(n, k): %o A333509 if n == 1: return 1 %o A333509 s = 0 %o A333509 for i in range(1, n + 1): %o A333509 for j in range(k * n - n + 1, k * n + 1): %o A333509 s += A(i, j, k, n) %o A333509 return s %o A333509 print([A333509(j + 1, i - j + 2) for i in range(9) for j in range(i + 1)]) %Y A333509 Columns k=2-3 give: A333510, A333511. %Y A333509 Rows n=1-3 give: A000012, A000079(n+1), 2*A082574(n+1)+1. %Y A333509 T(n,n) gives A121785(n-1). %K A333509 nonn,tabl %O A333509 1,3 %A A333509 _Seiichi Manyama_, Mar 25 2020