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 A271592 #14 Mar 28 2020 10:11:36 %S A271592 1,0,1,0,1,1,0,1,0,1,0,1,2,1,1,0,1,0,4,0,1,0,1,4,8,8,1,1,0,1,0,23,0, %T A271592 16,0,1,0,1,8,55,86,47,32,1,1,0,1,0,144,0,397,0,64,0,1,0,1,16,360,948, %U A271592 1770,1584,264,128,1,1,0,1,0,921,0,11658,0,6820,0,256,0,1 %N A271592 Array read by antidiagonals: T(n,m) = number of directed Hamiltonian walks from NW to SW corners on a grid with n rows and m columns. %H A271592 Andrew Howroyd, <a href="/A271592/b271592.txt">Antidiagonals n = 1..27, flattened</a> %F A271592 T(n,m)=0 for n odd and m even, T(1,n)=0 for n>1. %F A271592 T(2,n)=T(n,1)=T(2*n,2)=1, T(3,2*n+1)=T(n+1,3)=2^n. %e A271592 The start of the sequence as table: %e A271592 * 1 0 0 0 0 0 0 0 0 ... %e A271592 * 1 1 1 1 1 1 1 1 1 ... %e A271592 * 1 0 2 0 4 0 8 0 16 ... %e A271592 * 1 1 4 8 23 55 144 360 921 ... %e A271592 * 1 0 8 0 86 0 948 0 10444 ... %e A271592 * 1 1 16 47 397 1770 11658 59946 359962 ... %e A271592 * 1 0 32 0 1584 0 88418 0 4999752 ... %e A271592 * 1 1 64 264 6820 52387 909009 8934966 130373192 ... %e A271592 * 1 0 128 0 28002 0 7503654 0 2087813834 ... %e A271592 * ... %o A271592 (Python) %o A271592 # Using graphillion %o A271592 from graphillion import GraphSet %o A271592 import graphillion.tutorial as tl %o A271592 def A271592(n, k): %o A271592 if k == 1: return 1 %o A271592 universe = tl.grid(k - 1, n - 1) %o A271592 GraphSet.set_universe(universe) %o A271592 start, goal = 1, n %o A271592 paths = GraphSet.paths(start, goal, is_hamilton=True) %o A271592 return paths.len() %o A271592 print([A271592(j + 1, i - j + 1) for i in range(12) for j in range(i + 1)]) # _Seiichi Manyama_, Mar 28 2020 %Y A271592 Column 4 is aerated A014524, column 5 is A014585. %Y A271592 Rows include A181688, A181689. %Y A271592 Main diagonal is A000532. %Y A271592 Cf. A333580. %K A271592 nonn,tabl %O A271592 1,13 %A A271592 _Andrew Howroyd_, Apr 10 2016