A109123 a(n) = 4*(n+1)^2*(n+3)^2*(5*n^2 + 20*n + 12).

432, 9472, 64800, 269568, 842800, 2184192, 4953312, 10163200, 19288368, 34387200, 58238752, 94493952, 147841200, 224186368, 330847200, 476762112, 672713392, 931564800, 1268513568, 1701356800, 2250772272, 2940613632, 3798220000, 4854739968, 6145470000, 7710207232

Offset

0,1

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. 311).

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: 16*(27 + 403*x + 473*x^2 - 15*x^3 + 14*x^4 - 2*x^5)/(1-x)^7.

From Amiram Eldar, Jun 02 2022: (Start)

Sum_{n>=0} 1/a(n) = 197/864 - Pi^2/144 - (5/144)*sqrt(5/2)*Pi*cot(2*sqrt(2/5)*Pi).

Sum_{n>=0} (-1)^n/a(n) = -85/432 - Pi^2/288 - (5/144)*sqrt(5/2)*Pi*cosec(2*sqrt(2/5)*Pi). (End)

Maple

a:=n->4*(n+1)^2*(n+3)^2*(5*n^2+20*n+12): seq(a(n), n=0..28);

Mathematica

Table[4*(n + 1)^2*(n + 3)^2*(5*n^2 + 20*n + 12), {n, 0, 30}] (* Amiram Eldar, Jun 02 2022 *)

Crossrefs

Sequence in context: A223595 A223436 A230922 * A223688 A269183 A228105

Adjacent sequences: A109120 A109121 A109122 * A109124 A109125 A109126

Keyword

nonn

Author

Emeric Deutsch, Jun 19 2005

Status

approved