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

0,2

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

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

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 *)

Prog

(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

Crossrefs

Cf. A002212, A045868.

Sequence in context: A196810 A177755 A037965 * A090017 A257390 A104631

Adjacent sequences: A045899 A045900 A045901 * A045903 A045904 A045905

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 13 2004

Status

approved