A110692 Kekulé numbers for certain benzenoids.

1, 29, 275, 1498, 5846, 18250, 48546, 114480, 245751, 489247, 915629, 1627418, 2768740, 4536884, 7195828, 11091888, 16671645, 24502305, 35294647, 49928714, 69482402, 95263102, 128842550, 172095040, 227239155, 296883171, 384074289

Offset

0,2

References

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 243, M_n(LLAAAAL)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (n+1)*(n+2)*(n+3)*(155*n^4 +911*n^3 +2062*n^2 +2122*n +840)/7!.

G.f.: (8*x^4+54*x^3+71*x^2+21*x+1)/(x-1)^8. - Alois P. Heinz, Feb 27 2015

Maple

a:=n->(n+1)*(n+2)*(n+3)*(155*n^4+911*n^3+2062*n^2+2122*n+840)/5040: seq(a(n), n=0..31);

Mathematica

CoefficientList[Series[(8*x^4 + 54*x^3 + 71*x^2 + 21*x + 1)/(x - 1)^8, {x, 0, 50}], x] (* G. C. Greubel, Sep 06 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((8*x^4+54*x^3+71*x^2+21*x+1)/(x-1)^8) \\ G. C. Greubel, Sep 06 2017

Crossrefs

Sequence in context: A224408 A120823 A186263 * A081684 A142033 A142905

Adjacent sequences: A110689 A110690 A110691 * A110693 A110694 A110695

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 03 2005

Status

approved