A108670 a(n) = (n+1)(n+2)^3*(n+3)(n+4)(5n^2 + 16n + 15)/1440.

1, 27, 268, 1575, 6678, 22638, 65184, 165726, 381975, 813241, 1621620, 3060421, 5511324, 9531900, 15915264, 25763772, 40578813, 62368887, 93778300, 138238947, 200147794, 285072810, 399990240, 553556250, 756416115, 1021554261

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. 231, # 28).

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

Formula

From Colin Barker, Apr 23 2020: (Start)

G.f.: (1 + 3*x)*(1 + 15*x + 16*x^2 + 3*x^3) / (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->(n+1)*(n+2)^3*(n+3)*(n+4)*(5*n^2+16*n+15)/1440: seq(a(n), n=0..30);

Prog

(PARI) Vec((1 + 3*x)*(1 + 15*x + 16*x^2 + 3*x^3) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Apr 23 2020

Crossrefs

Sequence in context: A349507 A125390 A126548 * A136925 A181323 A136926

Adjacent sequences: A108667 A108668 A108669 * A108671 A108672 A108673

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 17 2005

Status

approved