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A186482 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.

%I A186482 #7 Jul 22 2025 10:21:51
%S A186482 256,205,205,1098,362,1098,1251,701,701,1251,4895,2049,4686,2049,4895,
%T A186482 5955,3442,4810,4810,3442,5955,20079,8223,20224,16762,20224,8223,
%U A186482 20079,27101,14492,21760,25633,25633,21760,14492,27101,84228,35081,82632,67714
%N A186482 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock commuting with each of its horizontal and vertical 2X2 subblock neighbors.
%C A186482 Table starts
%C A186482 ....256....205...1098....1251....4895....5955...20079....27101....84228
%C A186482 ....205....362....701....2049....3442....8223...14492....35081....64280
%C A186482 ...1098....701...4686....4810...20224...21760...82632...101108...344804
%C A186482 ...1251...2049...4810...16762...25633...67714..101305...286290...456113
%C A186482 ...4895...3442..20224...25633..107353..108025..433513...479785..1793817
%C A186482 ...5955...8223..21760...67714..108025..305089..418177..1286113..1812049
%C A186482 ..20079..14492..82632..101305..433513..418177.1849873..1894849..7687009
%C A186482 ..27101..35081.101108..286290..479785.1286113.1894849..5977657..8078233
%C A186482 ..84228..64280.344804..456113.1793817.1812049.7687009..8078233.34498177
%C A186482 .123227.150785.465884.1219034.2226665.5368065.8602033.25049545.36618769
%H A186482 R. H. Hardin, <a href="/A186482/b186482.txt">Table of n, a(n) for n = 1..1740</a>
%F A186482 Empirical, for every column: a(n)=2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-4)-3*a(n-5) for n>k+11
%e A186482 Some solutions for 4X3
%e A186482 ..0..0..2....2..0..0....0..1..0....0..3..0....2..0..0....0..0..1....3..0..0
%e A186482 ..0..0..0....0..0..0....2..0..1....1..0..3....0..2..0....0..0..0....0..3..0
%e A186482 ..0..0..0....0..0..0....0..2..0....0..1..0....2..0..2....0..0..0....2..0..3
%e A186482 ..3..3..3....1..0..0....1..0..2....3..0..1....0..2..0....0..0..3....0..2..1
%K A186482 nonn,tabl
%O A186482 1,1
%A A186482 _R. H. Hardin_ Feb 22 2011