A191006 - OEIS

%I #8 Dec 18 2015 18:17:39

%S 1,2,6,24,144,1296,16848,320112,8963136,367488576,22049314560,

%T 1940339681280,250303818885120,47307421769287680,13104155830092687360,

%U 5320287267017631068160,3165570923875490485555200

%N Number of n X n symmetric binary matrices with each 1 adjacent to exactly 1 diagonally neighboring 1

%H R. H. Hardin, <a href="/A191006/b191006.txt">Table of n, a(n) for n = 1..49</a>

%F Empirical: a(n) = a(n-1) * A000930(n+1), so from the formula there

%F Empirical: a(n) = product(sum(binomial(k+1-2*i,i), i=0..floor((k+1)/3)), k=1..n)

%e Some solutions for n=5

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

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

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

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

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

%Y a(n+1)/a(n) is A000930(n+2)

%K nonn

%O 1,2

%A _R. H. Hardin_ Jun 16 2011