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 A108684 a(n) = (n+1)*(n+2)*(n+3)*(19*n^3 + 111*n^2 + 200*n + 120)/720. 0
 1, 15, 93, 372, 1141, 2926, 6594, 13476, 25509, 45397, 76791, 124488, 194649, 295036, 435268, 627096, 884697, 1224987, 1667953, 2237004, 2959341, 3866346, 4993990, 6383260, 8080605, 10138401, 12615435, 15577408, 19097457, 23256696 (list; graph; refs; listen; history; text; internal format)
 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.233, # 10). LINKS Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA G.f.: (1 + 8*x + 9*x^2 + x^3)/(1-x)^7. a(n) = Sum_{k=0...n} A000217(n+1-k) * (A000292(n+1) - A000292(k)). - J. M. Bergot, Jun 07 2017 a(n) = A050405(n) + A181888(n+1). - R. J. Mathar, Jul 22 2022 MAPLE a:=n->(n+1)*(n+2)*(n+3)*(19*n^3+111*n^2+200*n+120)/720: seq(a(n), n=0..33); MATHEMATICA Table[(n + 1) (n + 2) (n + 3) (19 n^3 + 111 n^2 + 200 n + 120)/720, {n, 0, 29}] (* or *) CoefficientList[Series[(1 + 8 x + 9 x^2 + x^3)/(1 - x)^7, {x, 0, 29}], x] (* or *) Table[Sum[Binomial[(n + 1 - k) + 1, 2] Apply[Subtract, Map[Binomial[# + 2, 3] &, {n + 1, k}]], {k, 0, n}], {n, 0, 29}] (* Michael De Vlieger, Jun 08 2017 *) CROSSREFS Sequence in context: A329759 A041428 A052226 * A125325 A126483 A226766 Adjacent sequences: A108681 A108682 A108683 * A108685 A108686 A108687 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 19 2005 STATUS approved

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Last modified February 7 22:58 EST 2023. Contains 360132 sequences. (Running on oeis4.)