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A107971
a(n) = (n+1)(n+2)(n+3)(35n^3 + 153n^2 + 232n + 120)/720.
0
1, 18, 123, 523, 1673, 4424, 10206, 21246, 40821, 73546, 125697, 205569, 323869, 494144, 733244, 1061820, 1504857, 2092242, 2859367, 3847767, 5105793, 6689320, 8662490, 11098490, 14080365, 17701866, 22068333, 27297613, 33521013, 40884288
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230).
FORMULA
From R. J. Mathar, Apr 07 2008: (Start)
O.g.f.: -(1 + 11x + 18x^2 + 5x^3)/(-1+x)^7.
a(n) = A107962(n) - A107962(n-1). (End)
MAPLE
a:=n->(1/720)*(n+1)*(n+2)*(n+3)*(35*n^3+153*n^2+232*n+120): seq(a(n), n=0..35);
MATHEMATICA
Table[(n+1)(n+2)(n+3)(35n^3+153n^2+232n+120)/720, {n, 0, 30}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 18, 123, 523, 1673, 4424, 10206}, 30] (* Harvey P. Dale, Jan 05 2022 *)
CROSSREFS
Sequence in context: A223046 A037064 A077960 * A292314 A002424 A101378
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved