A107959 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2 + 5*n + 5)/720.

1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835, 412126, 806806, 1498861, 2662660, 4550560, 7518624, 12058236, 18834453, 28731990, 42909790, 62865187, 90508726, 128250760, 179101000, 246782250, 335859615, 451886526, 601568982

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 (9,-36,84,-126,126,-84,36,-9,1).

Formula

From Colin Barker, Apr 22 2020: (Start)

G.f.: (1 + 13*x + 28*x^2 + 13*x^3 + x^4) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

(End)

Sum_{n>=0} 1/a(n) = 120*Pi^2 - 144*sqrt(5)*Pi*tan(sqrt(5)*Pi/2) - 790. - Amiram Eldar, May 31 2022

Maple

a:=n->(1/720)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2+5*n+5): seq(a(n), n=0..30);

Mathematica

Table[(n+1)(n+2)^2(n+3)^2(n+4)(n^2+5n+5)/720, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835}, 30] (* Harvey P. Dale, Sep 27 2020 *)

Prog

(PARI) Vec((1 + 13*x + 28*x^2 + 13*x^3 + x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020

Crossrefs

Sequence in context: A231749 A072040 A022682 * A200936 A110690 A020923

Adjacent sequences: A107956 A107957 A107958 * A107960 A107961 A107962

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved