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

Offset: 0

Author

Emeric Deutsch, Jun 12 2005

Keywords

• nonn
• easy

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)

Crossrefs

Equals third right hand column of A161739 (RSEG2 triangle). - Johannes W. Meijer, Jun 18 2009

Cf. A000217, A000292.

Programs

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

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 *)

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

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