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Number of (n+2)X3 0..2 arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock
1

%I #5 Mar 31 2012 12:36:05

%S 19683,721,2917,6594,12122,20056,29303,35198,53611,85029,121783,

%T 199305,321297,465750,728568,1143162,1676187,2600987,4073323,6071427,

%U 9378717,14610267,21959403,33776511,52386811,79228491,121620695,188062383

%N Number of (n+2)X3 0..2 arrays with every 3X3 subblock commuting with each horizontal and vertical neighbor 3X3 subblock

%C Column 1 of A186568

%H R. H. Hardin, <a href="/A186560/b186560.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)+2*a(n-6)-2*a(n-7) for n>18

%e Some solutions for 4X3

%e ..1..2..2....0..0..0....0..1..0....0..0..0....0..0..0....1..1..0....1..2..0

%e ..2..2..0....0..0..0....0..0..1....0..0..0....0..0..0....0..0..0....0..2..0

%e ..0..2..2....2..2..0....2..0..0....2..1..0....0..0..0....0..0..0....0..1..0

%e ..2..1..0....0..2..2....0..2..0....2..1..1....2..0..2....0..1..2....0..0..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 23 2011