%I #6 Dec 18 2015 18:18:06
%S 1,5,172,38444,36567600,139088906848,2108407726540016,
%T 127364809805575916736,30660305986899859448541568,
%U 29412752846682454724638291977856
%N Number of n X n 0..3 symmetric matrices with every element equal to zero, one, two or three horizontal and vertical neighbors, and new values 0..3 introduced in lower triangle row major order
%H R. H. Hardin, <a href="/A210927/b210927.txt">Table of n, a(n) for n = 1..15</a>
%e Some solutions for n=4
%e ..0..0..1..1....0..1..2..1....0..0..2..1....0..0..1..0....0..1..1..0
%e ..0..0..2..2....1..1..2..1....0..1..3..3....0..1..2..2....1..0..0..1
%e ..1..2..3..1....2..2..0..3....2..3..2..0....1..2..2..0....1..0..0..1
%e ..1..2..1..0....1..1..3..3....1..3..0..0....0..2..0..2....0..1..1..0
%K nonn
%O 1,2
%A _R. H. Hardin_ Mar 29 2012