OFFSET
0,2
COMMENTS
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Mar 13 2004
STATUS
approved