A045635 Catafusenes (see references for precise definition).

0, 0, 1, 9, 57, 315, 1629, 8127, 39718, 191754, 919035, 4385799, 20879100, 99276840, 471848195, 2242864575, 10665998760, 50757180840, 241743946635, 1152434818755, 5499250360025, 26268118117731, 125602004765391

Offset

1,4

Comments

The sequence without the initial 0's is the 3-fold convolution of A002212(n), (n=1,2,...). - Emeric Deutsch, Mar 13 2004

Links

Table of n, a(n) for n=1..23.

B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes, Monat. f. Chemie, 125 (1994), 1327-1337.

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.: (zM)^3, where M = (1 - 3*z - sqrt(1 - 6*z + 5*z^2))/(2*z^2). - Emeric Deutsch, Mar 13 2004

a(n) = (3/(n+1))*Sum_{m=0..n-2} C(n+1,m)*C(2*n-2*m+2,n-m-2). - Vladimir Kruchinin Oct 18 2022

a(n) = A003517(n) * hypergeom([-n - 4, 2 - n], [-n - 1/2], -1/4). - Peter Luschny, Oct 23 2022

Maple

Z:=(1-8*z+24*z^2-16*z^3-(1-6*z+8*z^2)*sqrt(1-6*z+5*z^2))/2: Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=4..26); # Zerinvary Lajos, Jan 01 2007
a := n -> A003517(n) * hypergeom([-n - 4, 2 - n], [-n - 1/2], -1/4):
seq(simplify(a(n)), n = 0..22); # Peter Luschny, Oct 23 2022

Crossrefs

Cf. A002212, A003517.

Sequence in context: A192054 A045720 A014916 * A026896 A080961 A163919

Adjacent sequences: A045632 A045633 A045634 * A045636 A045637 A045638

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 13 2004

Status

approved