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A139678 Number of n X n symmetric binary matrices with no row sum greater than 2. 1
1, 2, 8, 45, 315, 2634, 25518, 280257, 3434595, 46400310, 684374076, 10933866027, 187983528813, 3458845917990, 67787903801790, 1409293876400019, 30968525550983913, 717023025711440082, 17442766619178969600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Problem discussed on the Art of Problem Solving forum

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

CROSSREFS

Sequence in context: A002833 A139015 A197996 * A152401 A009345 A084553

Adjacent sequences:  A139675 A139676 A139677 * A139679 A139680 A139681

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 13 2008

STATUS

approved

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Last modified November 23 22:48 EST 2014. Contains 249866 sequences.