A108683 a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n^2 + 20*n + 15)/360.

1, 14, 83, 322, 966, 2436, 5418, 10956, 20559, 36322, 61061, 98462, 153244, 231336, 340068, 488376, 687021, 948822, 1288903, 1724954, 2277506, 2970220, 3830190, 4888260, 6179355, 7742826, 9622809, 11868598, 14535032, 17682896, 21379336, 25698288, 30720921

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. 233, # 8).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1+x)*(1+6*x)/(1-x)^7.

Maple

G:=factor(sum(a(n)*z^n, n=0..infinity)); series(G, z=0, 37);

Mathematica

Table[(1+n) (2+n) (3+n) (4+n) (15+n (20+7 n))/360, {n, 0, 40}] (* Harvey P. Dale, Aug 23 2020 *)

Crossrefs

Sequence in context: A176010 A250562 A166819 * A376290 A323415 A166389

Adjacent sequences: A108680 A108681 A108682 * A108684 A108685 A108686

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 18 2005

Status

approved