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A186558 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock commuting with any of its horizontal and vertical 2X2 subblock neighbors.

%I A186558 #7 Jul 22 2025 10:25:09
%S A186558 256,3891,3891,60074,227890,60074,927477,13360840,13360840,927477,
%T A186558 14319230,783375343,2976803436,783375343,14319230,221073168,
%U A186558 45931015744,663296784123,663296784123,45931015744,221073168,3413126694
%N A186558 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock commuting with any of its horizontal and vertical 2X2 subblock neighbors.
%C A186558 Table starts
%C A186558 .........256............3891.............60074.............927477
%C A186558 ........3891..........227890..........13360840..........783375343
%C A186558 .......60074........13360840........2976803436.......663296784123
%C A186558 ......927477.......783375343......663296784123....561714653720250
%C A186558 ....14319230.....45931015744...147795682647630.475681559860717916
%C A186558 ...221073168...2693039069563.32931888185295104
%C A186558 ..3413126694.157898954845170
%C A186558 .52694924343
%H A186558 R. H. Hardin, <a href="/A186558/b186558.txt">Table of n, a(n) for n = 1..40</a>
%e A186558 Some solutions for 4X3
%e A186558 ..0..0..0....3..0..0....2..0..0....0..0..0....0..0..0....1..0..0....1..0..0
%e A186558 ..3..1..0....3..2..0....1..1..0....1..1..0....3..2..0....0..3..0....1..2..0
%e A186558 ..3..0..3....1..3..3....3..2..3....3..1..0....0..2..0....2..1..2....0..0..0
%e A186558 ..2..1..3....0..1..2....0..0..0....1..3..0....0..3..1....2..3..2....3..1..2
%K A186558 nonn,tabl
%O A186558 1,1
%A A186558 _R. H. Hardin_ Feb 23 2011