A108178 a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(7n^2 + 23n + 20)/2880.

1, 25, 235, 1330, 5488, 18228, 51660, 129690, 295845, 624481, 1236235, 2318680, 4153240, 7149520, 11888304, 19174572, 30101985, 46130385, 69177955, 101729782, 146964664, 208902100, 292571500, 404205750, 551461365, 743667561, 992106675

Offset

0,2

Comments

Kekulé numbers for certain benzenoids.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230, no. 20).

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

From Colin Barker, Apr 22 2020: (Start)

G.f.: (1 + 16*x + 46*x^2 + 31*x^3 + 4*x^4) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

(End)

Maple

a:=(n+1)*(n+2)^2*(n+3)^2*(n+4)*(7*n^2+23*n+20)/2880: seq(a(n), n=0..30);

Mathematica

Table[(n+1)(n+2)^2(n+3)^2(n+4)(7n^2+23n+20)/2880, {n, 0, 50}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 25, 235, 1330, 5488, 18228, 51660, 129690, 295845}, 50] (* Harvey P. Dale, Aug 16 2021 *)

Prog

(PARI) Vec((1 + 16*x + 46*x^2 + 31*x^3 + 4*x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020

Crossrefs

Sequence in context: A221930 A160222 A088890 * A278849 A294290 A352304

Adjacent sequences: A108175 A108176 A108177 * A108179 A108180 A108181

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 13 2005

Status

approved