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A107963

a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(5*n^2 + 19*n + 15)/360.

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

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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. 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