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 A375861 #7 Sep 03 2024 23:03:31 %S A375861 1,1,1,1,2,1,1,5,5,1,1,9,19,9,1,1,19,63,63,19,1,1,35,192,298,192,35,1, %T A375861 1,71,576,1246,1246,576,71,1,1,135,1698,4857,6351,4857,1698,135,1,1, %U A375861 271,5042,18768,29467,29467,18768,5042,271,1,1,527,14963,72968,134397,152516,134397,72968,14963,527,1 %N A375861 Array T(n,m) read by antidiagonals: In an n X m grid draw straight walls between cells, starting at a border, such that the resulting figure is connected and has only one-cell wide paths; T(n,m) is the number of solutions up to symmetries of the rectangle. %C A375861 See A375770 and A375860 for additional explanation and illustration of solutions. %H A375861 Andrew Howroyd, <a href="/A375861/b375861.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals) %F A375861 T(n,m) = T(m,n). %e A375861 Array begins: %e A375861 =============================================== %e A375861 n/m | 1 2 3 4 5 6 7 ... %e A375861 ----+------------------------------------------ %e A375861 1 | 1 1 1 1 1 1 1 ... %e A375861 2 | 1 2 5 9 19 35 71 ... %e A375861 3 | 1 5 19 63 192 576 1698 ... %e A375861 4 | 1 9 63 298 1246 4857 18768 ... %e A375861 5 | 1 19 192 1246 6351 29467 134397 ... %e A375861 6 | 1 35 576 4857 29467 152516 763479 ... %e A375861 7 | 1 71 1698 18768 134397 763479 3982186 ... %e A375861 ... %o A375861 (PARI) \\ A375861(n,m) defined in PARI link in A375770. %Y A375861 Main diagonal is A375860. %Y A375861 Cf. A375858 (not reduced for symmetry). %K A375861 nonn,tabl %O A375861 1,5 %A A375861 _Andrew Howroyd_, Aug 31 2024