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A110691 Kekulé numbers for certain benzenoids. 1
1, 45, 632, 4825, 25227, 101822, 340416, 986094, 2551725, 6028099, 13209768, 27179087, 53000311, 98685900, 176508416, 304743564, 509943033, 829849833, 1317083800, 2043740853, 3107066435, 4636381354, 6801456960, 9822556250 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)