A107968 a(n) = (n+1)*(n+2)^3*(n+3)^2*(n+4)*(3n+5)/1440.

1, 24, 220, 1225, 4998, 16464, 46368, 115830, 263175, 553696, 1093092, 2045407, 3656380, 6283200, 10431744, 16802460, 26346141, 40330920, 60421900, 88774917, 128146018, 182018320, 254748000, 351731250, 479594115, 646407216, 861927444

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. 230).

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 + 15*x + 40*x^2 + 25*x^3 + 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)

From Amiram Eldar, May 31 2022: (Start)

Sum_{n>=0} 1/a(n) = 7895/7 + 10935*sqrt(3)*Pi/14 + 150*Pi^2 - 98415*log(3)/14 + 720*zeta(3).

Sum_{n>=0} (-1)^n/a(n) = 2875/7 + 10935*sqrt(3)*Pi/7 - 105*Pi^2 - 72960*log(2)/7 - 540*zeta(3). (End)

Maple

a:=n->(1/1440)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(3*n+5): seq(a(n), n=0..30);

Mathematica

Table[(n + 1)*(n + 2)^3*(n + 3)^2*(n + 4)*(3 n + 5)/1440, {n, 0, 25}] (* Amiram Eldar, May 31 2022 *)

Prog

(PARI) Vec((1 + 15*x + 40*x^2 + 25*x^3 + 3*x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020

Crossrefs

Sequence in context: A042112 A297679 A202073 * A269777 A024302 A181710

Adjacent sequences: A107965 A107966 A107967 * A107969 A107970 A107971

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved