A045902 Catafusenes (see reference for precise definition).

1, 4, 18, 80, 355, 1580, 7066, 31772, 143645, 652860, 2981910, 13682328, 63046776, 291646860, 1353967250, 6306552800, 29464361530, 138045441260, 648449195350, 3053348997200, 14409512770575, 68143962854836, 322886537205062, 1532716400556220, 7288075248828605, 34710221395625380

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

4-fold convolution of A002212. Convolution of A045868 with itself. - Emeric Deutsch, Mar 13 2004

References

• S. J. Cyvin et al., Enumeration and classification of certain polygonal systems... : annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A002212, A045868.

Programs

Maple

a := n->(4/n)*sum(binomial(n,j)*binomial(2*j+3,j-1),j=1..n): 1,seq(a(n),n=1..22);

Mathematica

Table[SeriesCoefficient[(1-x-Sqrt[1-6*x+5*x^2])^4/(16*x^4),{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 08 2012 *)

PARI

x='x+O('x^66); Vec((1-x-sqrt(1-6*x+5*x^2))^4/(16*x^4)) \\ Joerg Arndt, May 04 2013

Formula

G.f.: (1 - x - sqrt(1-6*x+5*x^2))^4/(16*x^4). - Emeric Deutsch, Mar 13 2004

a(n) = (4/n)*Sum_{j=1..n} binomial(n, j)*binomial(2j+3, j-1) for n >= 1. - Emeric Deutsch, Mar 25 2004

Recurrence: (n+1)*(n+4)*a(n) = (6*n^2+19*n+19)*a(n-1) - 5*(n-2)*(n+2)*a(n-2). - Vaclav Kotesovec, Oct 08 2012

a(n) ~ 16*5^(n+1/2)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 08 2012

Extensions

More terms from Emeric Deutsch, Mar 13 2004