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 A107963 a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(5*n^2 + 19*n + 15)/360. 5
 1, 13, 73, 273, 798, 1974, 4326, 8646, 16071, 28171, 47047, 75439, 116844, 175644, 257244, 368220, 516477, 711417, 964117, 1287517, 1696618, 2208690, 2843490, 3623490, 4574115, 5723991, 7105203, 8753563, 10708888, 13015288, 15721464 (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. 229). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1) FORMULA G.f.: ( -1-6*x-3*x^2 ) / (x-1)^7 . - R. J. Mathar, Feb 16 2011 a(n) = Sum_{i=0..n+1} A000217(i)*A000292(i) with a(-1)=0. - Bruno Berselli, Jul 20 2015 MAPLE a:=n->(1/360)*(n+1)*(n+2)*(n+3)*(n+4)*(5*n^2+19*n+15): seq(a(n), n=0..36); MATHEMATICA LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 13, 73, 273, 798, 1974, 4326}, 40] (* Vincenzo Librandi, Apr 23 2017 *) PROG (PARI) a(n)=(n+1)*(n+2)*(n+3)*(n+4)*(5*n^2+19*n+15)/360 \\ Charles R Greathouse IV, Oct 16 2015 (MAGMA) [(n+1)*(n+2)*(n+3)*(n+4)*(5*n^2+19*n+15)/360: n in [0..30]]; // Vincenzo Librandi, Apr 23 2017 CROSSREFS Equals third right hand column of A161739 (RSEG2 triangle). - Johannes W. Meijer, Jun 18 2009 Cf. A000217, A000292. Sequence in context: A060886 A081586 A143008 * A006230 A066110 A020527 Adjacent sequences:  A107960 A107961 A107962 * A107964 A107965 A107966 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)