A139678 Number of n X n symmetric binary matrices with no row sum greater than 2.

1, 2, 8, 45, 315, 2634, 25518, 280257, 3434595, 46400310, 684374076, 10933866027, 187983528813, 3458845917990, 67787903801790, 1409293876400019, 30968525550983913, 717023025711440082, 17442766619178969600, 444704318660973471885, 11855331996299677291131

Offset: 0

Author

R. H. Hardin, Jun 13 2008

Keywords

• nonn

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..200
• Art of Problem Solving forum, A recursive formula please

Crossrefs

Column k=2 of A334548.

Programs

Maple

n:=18: G:=taylor((1/sqrt(1-x))*exp((6*x + x^2 + x^3)/(4 - 4*x)),x=0,n+1): seq(coeff(G,x,m)*m!,m=0..n); # Nathaniel Johnston, Apr 19 2011

PARI

seq(n) = {Vec(serlaplace(exp( (6*x + x^2 + x^3)/(4*(1 - x)) + O(x*x^n) ) / sqrt(1 - x + O(x*x^n))))} \\ Andrew Howroyd, May 08 2020

Formula

E.g.f.: exp( (6*x + x^2 + x^3)/(4*(1 - x)) ) / sqrt(1 - x). - Joel B. Lewis, Apr 17 2011, corrected by Vaclav Kotesovec, Aug 13 2013

a(n) ~ n^n*exp(2*sqrt(2*n)-n-7/4)/sqrt(2) * (1+17/(6*sqrt(2*n))). - Vaclav Kotesovec, Aug 13 2013

Recurrence: 2*a(n) = 4*n*a(n-1) - 2*(n-2)*(n-1)*a(n-2) + (n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Aug 13 2013

Extensions

a(19)-a(20) added from b-file by Andrew Howroyd, May 08 2020