A110693 Kekulé numbers for certain benzenoids.

1, 36, 448, 3175, 15786, 61446, 199872, 566676, 1441275, 3356782, 7268976, 14805583, 28621684, 52892100, 93977088, 161303616, 268510869, 434915472, 687359200, 1062509679, 1609692766, 2394343930, 3502175040, 5044162500

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, H*(3,5,n)).

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = 2*(n+1)*(n+2)^3*(n+3)*(n+4)*(25*n^3 + 142*n^2 + 295*n + 210)/8!.

G.f.: ( 1+26*x+133*x^2+195*x^3+86*x^4+9*x^5 )/(1-x)^10. - R. J. Mathar, Nov 01 2015

Maple

a:=n->(n+1)*(n+2)^3*(n+3)*(n+4)*(25*n^3+142*n^2+295*n+210)/20160: seq(a(n), n=0..27);

Mathematica

CoefficientList[Series[(1+26*x+133*x^2+195*x^3+86*x^4+9*x^5)/(1-x)^10, {x, 0, 50}], x] (* G. C. Greubel, Sep 06 2017 *)

Prog

(Python)
A110693_list, m = [], [450, -816, 508, -121, 10, 1, 1, 1, 1, 1]
for _ in range(10001):
    A110693_list.append(m[-1])
    for i in range(9):
        m[i+1] += m[i] # Chai Wah Wu, Jun 12 2016
(PARI) x='x+O(x^50); Vec((1+26*x+133*x^2+195*x^3+86*x^4+9*x^5)/(1-x)^10) \\ G. C. Greubel, Sep 06 2017

Crossrefs

Sequence in context: A281403 A256149 A244498 * A104671 A323549 A128986

Adjacent sequences: A110690 A110691 A110692 * A110694 A110695 A110696

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 03 2005

Status

approved