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%I #7 Sep 03 2024 23:03:31
%S 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 1,71,576,1246,1246,576,71,1,1,135,1698,4857,6351,4857,1698,135,1,1,
%U 271,5042,18768,29467,29467,18768,5042,271,1,1,527,14963,72968,134397,152516,134397,72968,14963,527,1
%N 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 See A375770 and A375860 for additional explanation and illustration of solutions.
%H Andrew Howroyd, <a href="/A375861/b375861.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)
%F T(n,m) = T(m,n).
%e Array begins:
%e ===============================================
%e n/m | 1 2 3 4 5 6 7 ...
%e ----+------------------------------------------
%e 1 | 1 1 1 1 1 1 1 ...
%e 2 | 1 2 5 9 19 35 71 ...
%e 3 | 1 5 19 63 192 576 1698 ...
%e 4 | 1 9 63 298 1246 4857 18768 ...
%e 5 | 1 19 192 1246 6351 29467 134397 ...
%e 6 | 1 35 576 4857 29467 152516 763479 ...
%e 7 | 1 71 1698 18768 134397 763479 3982186 ...
%e ...
%o (PARI) \\ A375861(n,m) defined in PARI link in A375770.
%Y Main diagonal is A375860.
%Y Cf. A375858 (not reduced for symmetry).
%K nonn,tabl
%O 1,5
%A _Andrew Howroyd_, Aug 31 2024