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A110692
Kekulé numbers for certain benzenoids.
1
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)).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 03 2005
STATUS
approved