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Half the number of n X n symmetric binary matrices with no element unequal to a strict majority of its diagonal, vertical and horizontal neighbors.
0

%I #8 Mar 15 2023 11:18:30

%S 1,1,3,10,42,244,2031,22714,342292,6943430,188479666,6843502049,

%T 331910774405,21483424837024,1854744805774187,213498320443922663,

%U 32758157589935274374

%N Half the number of n X n symmetric binary matrices with no element unequal to a strict majority of its diagonal, vertical and horizontal neighbors.

%e Some solutions for n=5 with a(1,1)=0:

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

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

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

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

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

%K nonn

%O 1,3

%A _R. H. Hardin_, May 16 2011