A110691 Kekulé numbers for certain benzenoids.

1, 45, 632, 4825, 25227, 101822, 340416, 986094, 2551725, 6028099, 13209768, 27179087, 53000311, 98685900, 176508416, 304743564, 509943033, 829849833, 1317083800, 2043740853, 3107066435, 4636381354, 6801456960, 9822556250

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*(4,4,n)).

Links

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

Formula

a(n) = (n+1)*(n+2)^3*(n+3)*(13*n^4 + 104*n^3 + 311*n^2 + 412*n + 210)/7!.

G.f.: (x^6+35*x^5+227*x^4+410*x^3+227*x^2+35*x+1)/(1-x)^10. - Alois P. Heinz, Feb 27 2015

Maple

a:=n->(n+1)*(n+2)^3*(n+3)*(13*n^4+104*n^3+311*n^2+412*n+210)/5040: seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[(x^6 + 35*x^5 + 227*x^4 + 410*x^3 + 227*x^2 + 35*x + 1)/(x - 1)^10, {x, 0, 50}], x] (* G. C. Greubel, Sep 06 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((x^6+35*x^5+227*x^4+410*x^3+227*x^2+35*x+1)/(1-x)^10) \\ G. C. Greubel, Sep 06 2017

Crossrefs

Sequence in context: A090024 A282767 A160234 * A296540 A105251 A099632

Adjacent sequences: A110688 A110689 A110690 * A110692 A110693 A110694

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 03 2005

Status

approved