%I #15 Dec 18 2015 18:17:12
%S 1,4,20,100,720,7920,156960,4978909,162844632,9658482053,917891979225,
%T 113051563311936,21440096665285608,6394092372716939840,
%U 2723634378368868283440,1747667851609071536512000
%N Number of n X n symmetric binary matrices with each element either the sum mod 2 of its diagonal neighbors or the sum mod 2 of its antidiagonal neighbors
%H R. H. Hardin, <a href="/A093440/b093440.txt">Table of n, a(n) for n = 1..21</a>
%e Some solutions for 5X5
%e ..0..0..1..1..0....0..0..1..0..0....1..1..1..1..1....0..0..1..1..1
%e ..0..0..0..1..1....0..1..0..1..0....1..1..1..1..0....0..0..1..1..1
%e ..1..0..1..0..1....1..0..1..1..1....1..1..0..0..0....1..1..0..1..0
%e ..1..1..0..1..0....0..1..1..0..1....1..1..0..0..1....1..1..1..0..0
%e ..0..1..1..0..0....0..0..1..1..0....1..0..0..1..0....1..1..0..0..0
%K nonn
%O 1,2
%A _R. H. Hardin_ Jun 26 2011