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 A107966 a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(5n^2 + 23n + 30)/8640. 1
 1, 29, 320, 2100, 9898, 37044, 116928, 323730, 807675, 1851421, 3955952, 7966322, 15249780, 27941200, 49273344, 84012300, 139021461, 223980645, 352290400, 542195192, 818163038, 1212563220, 1767688000, 2538168750, 3593841615 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for certain benzenoids. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229). Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA a(0)=1, a(1)=29, a(2)=320, a(3)=2100, a(4)=9898, a(5)=37044, a(6)=116928, a(7)=323730, a(8)=807675, a(9)=1851421, a(n)=10*a(n-1)- 45*a(n-2)+ 120*a(n-3)- 210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)- 45*a(n-8)+ 10*a(n-9)-a(n-10). - Harvey P. Dale, Apr 18 2016 G.f.: (1 + 19*x + 75*x^2 + 85*x^3 + 28*x^4 + 2*x^5) / (1 - x)^10. - Colin Barker, Apr 22 2020 MAPLE a:=n->(1/8640)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(5*n^2+23*n+30): seq(a(n), n=0..26); MATHEMATICA Table[(n+1)(n+2)^3(n+3)^2(n+4)(5n^2+23n+30)/8640, {n, 0, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 29, 320, 2100, 9898, 37044, 116928, 323730, 807675, 1851421}, 30] (* Harvey P. Dale, Apr 18 2016 *) PROG (PARI) Vec((1 + 19*x + 75*x^2 + 85*x^3 + 28*x^4 + 2*x^5) / (1 - x)^10 + O(x^30)) \\ Colin Barker, Apr 22 2020 CROSSREFS Sequence in context: A165616 A142380 A042632 * A057131 A160442 A125417 Adjacent sequences:  A107963 A107964 A107965 * A107967 A107968 A107969 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)