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A186462 T(n,k)=Number of (n+1)X(k+1) binary arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

%I A186462 #7 Jul 22 2025 10:20:18
%S A186462 16,21,21,42,30,42,61,51,51,61,106,88,111,88,106,151,128,162,162,128,
%T A186462 151,245,197,270,309,270,197,245,359,292,362,449,449,362,292,359,567,
%U A186462 457,590,673,797,673,590,457,567,840,688,846,945,1061,1061,945,846,688,840,1301
%N A186462 T(n,k)=Number of (n+1)X(k+1) binary arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.
%C A186462 Table starts
%C A186462 ..16...21...42...61..106..151...245...359...567...840..1301...1941...2977
%C A186462 ..21...30...51...88..128..197...292...457...688..1058..1589...2424...3651
%C A186462 ..42...51..111..162..270..362...590...846..1362..1998..3122...4622...7126
%C A186462 ..61...88..162..309..449..673...945..1493..2201..3473..5177...7993..11949
%C A186462 .106..128..270..449..797.1061..1681..2285..3681..5281..8437..12401..19317
%C A186462 .151..197..362..673.1061.1693..2377..3677..5073..7977.11533..18221..26957
%C A186462 .245..292..590..945.1681.2377..4121..5633..8893.11977.19037..27133..43249
%C A186462 .359..457..846.1493.2285.3677..5633..9477.13245.20281.27573..43177..62025
%C A186462 .567..688.1362.2201.3681.5073..8893.13245.22933.31217.48241..64785.102213
%C A186462 .840.1058.1998.3473.5281.7977.11977.20281.31217.52197.71885.109497.148069
%H A186462 R. H. Hardin, <a href="/A186462/b186462.txt">Table of n, a(n) for n = 1..2449</a>
%F A186462 Empirical, for every column: a(n)=2*a(n-1)-2*a(n-3)+2*a(n-4)-a(n-5) for n>max(8,k+6)
%e A186462 Some solutions for 4X3
%e A186462 ..1..0..0....1..1..0....1..0..1....1..0..1....0..1..0....1..0..1....0..0..0
%e A186462 ..1..0..0....0..0..1....0..1..0....0..1..0....0..0..1....0..1..0....0..0..0
%e A186462 ..0..1..0....0..0..0....1..0..1....1..0..1....0..0..0....0..0..1....0..0..0
%e A186462 ..0..0..1....1..0..0....0..1..0....0..1..1....1..0..0....0..0..0....0..0..1
%K A186462 nonn,tabl
%O A186462 1,1
%A A186462 _R. H. Hardin_ Feb 22 2011