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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS KekulĂ© numbers for certain benzenoids. REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230). LINKS Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1). 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 Adjacent sequences:  A107968 A107969 A107970 * A107972 A107973 A107974 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)