A107956 a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(5n^2 + 21n + 20)/2880.

1, 23, 205, 1120, 4508, 14700, 41076, 101970, 230505, 482911, 949949, 1772134, 3159520, 5416880, 8975184, 14430348, 22590297, 34531455, 51665845, 75820052, 109327372, 155134540, 216924500, 299256750, 407726865, 549146871, 731748213

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 + 14*x + 34*x^2 + 19*x^3 + 2*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)

Maple

a:=n->(1/2880)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(5*n^2+21*n+20): seq(a(n), n=0..30);

Prog

(PARI) Vec((1 + 14*x + 34*x^2 + 19*x^3 + 2*x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020

Crossrefs

Sequence in context: A367182 A221670 A128334 * A022683 A042020 A263521

Adjacent sequences: A107953 A107954 A107955 * A107957 A107958 A107959

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved