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A045890 Catafusenes (see reference for precise definition). 1
1, 3, 12, 49, 204, 864, 3714, 16170, 71178, 316303, 1417248, 6396273, 29051856, 132700725, 609200640, 2809373915, 13008512040, 60457182345, 281919911460, 1318666411635, 6185356518660, 29088241615910, 137121834221346, 647821223533044, 3066862717614234, 14546629647573969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

3-fold convolution of A002212. - Emeric Deutsch, Mar 13 2004

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (1 - x - sqrt(1-6*x+5*x^2))^3/(8*x^3). - Emeric Deutsch, Mar 13 2004

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

Recurrence: (n+2)*(n+3)*a(n) = 2*(n+2)*(3*n+4)*a(n-1) - 5*(n-2)*(n+3)*a(n-2). - Vaclav Kotesovec, Oct 08 2012

a(n) ~ 6*5^(n+1/2)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 08 2012

MAPLE

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

MATHEMATICA

a[n_] := 3*(Hypergeometric2F1[5/2, 1-n, 5, -4] + (n-1)*Hypergeometric2F1[7/2, 2-n, 6, -4]); a[0]=1; Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Jun 13 2012, after Emeric Deutsch *)

CoefficientList[Series[(1-x-Sqrt[1-6x+5x^2])^3/(8x^3), {x, 0, 30}], x] (* Harvey P. Dale, Feb 07 2015 *)

PROG

(PARI) x='x+O('x^66); Vec((1-x-sqrt(1-6*x+5*x^2))^3/(8*x^3)) \\ Joerg Arndt, May 04 2013

CROSSREFS

Cf. A002212.

Sequence in context: A037646 A012772 A012864 * A049673 A052703 A151170

Adjacent sequences:  A045887 A045888 A045889 * A045891 A045892 A045893

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Emeric Deutsch, Mar 13 2004

STATUS

approved

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Last modified December 1 16:24 EST 2020. Contains 338845 sequences. (Running on oeis4.)