A191006 Number of n X n symmetric binary matrices with each 1 adjacent to exactly 1 diagonally neighboring 1

1, 2, 6, 24, 144, 1296, 16848, 320112, 8963136, 367488576, 22049314560, 1940339681280, 250303818885120, 47307421769287680, 13104155830092687360, 5320287267017631068160, 3165570923875490485555200

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..49

Formula

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

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

Example

Some solutions for n=5
..0..0..0..1..0....0..0..0..1..0....1..1..1..1..0....1..0..0..1..0
..0..0..1..0..1....0..0..0..0..1....1..1..1..1..1....0..1..0..1..1
..0..1..1..1..0....0..0..0..1..0....1..1..0..0..0....0..0..0..1..1
..1..0..1..1..0....1..0..1..0..1....1..1..0..1..0....1..1..1..1..1
..0..1..0..0..0....0..1..0..1..0....0..1..0..0..1....0..1..1..1..1

Crossrefs

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

Sequence in context: A375812 A375808 A258325 * A082471 A275594 A013010

Adjacent sequences: A191003 A191004 A191005 * A191007 A191008 A191009

Keyword

nonn

Author

R. H. Hardin Jun 16 2011

Status

approved