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

0,2

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..200

Art of Problem Solving forum, A recursive formula please

Formula

E.g.f.: exp( (6x + 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

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

Prog

(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

Crossrefs

Column k=2 of A334548.

Sequence in context: A316367 A308599 A367316 * A290445 A152401 A325138

Adjacent sequences: A139675 A139676 A139677 * A139679 A139680 A139681

Keyword

nonn

Author

R. H. Hardin, Jun 13 2008

Extensions

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

Status

approved