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Number of (n+4)X8 binary arrays with every 5X5 subblock commuting with each horizontal and vertical neighbor 5X5 subblock
1

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

%S 42120,3455,5813,19248,54040,90664,98376,99820,101072,102332,103620,

%T 105172,108332,117492,152956,244561,344142,446775,556660,694109,

%U 888987,1093393,1304011,1531041,1821099,2260191,2808392,3465438,4248781,5232601

%N Number of (n+4)X8 binary arrays with every 5X5 subblock commuting with each horizontal and vertical neighbor 5X5 subblock

%C Column 4 of A186609

%H R. H. Hardin, <a href="/A186604/b186604.txt">Table of n, a(n) for n = 1..117</a>

%F Empirical: a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-5)-a(n-6)-a(n-8)+a(n-9)+a(n-10)-a(n-13) for n>18

%e Some solutions for 6X8

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 24 2011