A107971 a(n) = (n+1)(n+2)(n+3)(35n^3 + 153n^2 + 232n + 120)/720.

1, 18, 123, 523, 1673, 4424, 10206, 21246, 40821, 73546, 125697, 205569, 323869, 494144, 733244, 1061820, 1504857, 2092242, 2859367, 3847767, 5105793, 6689320, 8662490, 11098490, 14080365, 17701866, 22068333, 27297613, 33521013, 40884288

Offset

0,2

Comments

Kekulé numbers for certain benzenoids.

References

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

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

From R. J. Mathar, Apr 07 2008: (Start)

O.g.f.: -(1 + 11x + 18x^2 + 5x^3)/(-1+x)^7.

a(n) = A107962(n) - A107962(n-1). (End)

Maple

a:=n->(1/720)*(n+1)*(n+2)*(n+3)*(35*n^3+153*n^2+232*n+120): seq(a(n), n=0..35);

Mathematica

Table[(n+1)(n+2)(n+3)(35n^3+153n^2+232n+120)/720, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 18, 123, 523, 1673, 4424, 10206}, 30] (* Harvey P. Dale, Jan 05 2022 *)

Crossrefs

Sequence in context: A223046 A037064 A077960 * A292314 A002424 A101378

Adjacent sequences: A107968 A107969 A107970 * A107972 A107973 A107974

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved