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%I #12 Sep 03 2024 23:03:35
%S 1,1,1,1,4,1,1,11,11,1,1,26,56,26,1,1,57,212,212,57,1,1,120,701,1112,
%T 701,120,1,1,247,2179,4793,4793,2179,247,1,1,502,6600,19082,25000,
%U 19082,6600,502,1,1,1013,19808,74368,116852,116852,74368,19808,1013,1
%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.
%C See A375770 and A375817 for additional explanation and illustration of solutions.
%C This sequence counts a subset of the spanning trees enumerated in A116469.
%H Andrew Howroyd, <a href="/A375858/b375858.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 4 11 26 57 120 247 ...
%e 3 | 1 11 56 212 701 2179 6600 ...
%e 4 | 1 26 212 1112 4793 19082 74368 ...
%e 5 | 1 57 701 4793 25000 116852 535776 ...
%e 6 | 1 120 2179 19082 116852 607712 3048668 ...
%e 7 | 1 247 6600 74368 535776 3048668 15918280 ...
%e ...
%o (PARI) \\ A375858(n,m) defined in PARI link in A375770.
%Y Main diagonal is A375817.
%Y Cf. A116469, A375770, A375859, A375860, A375861.
%K nonn,tabl
%O 1,5
%A _Andrew Howroyd_, Aug 31 2024