A107966 a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(5n^2 + 23n + 30)/8640.

1, 29, 320, 2100, 9898, 37044, 116928, 323730, 807675, 1851421, 3955952, 7966322, 15249780, 27941200, 49273344, 84012300, 139021461, 223980645, 352290400, 542195192, 818163038, 1212563220, 1767688000, 2538168750, 3593841615

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(0)=1, a(1)=29, a(2)=320, a(3)=2100, a(4)=9898, a(5)=37044, a(6)=116928, a(7)=323730, a(8)=807675, a(9)=1851421, a(n)=10*a(n-1)- 45*a(n-2)+ 120*a(n-3)- 210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)- 45*a(n-8)+ 10*a(n-9)-a(n-10). - Harvey P. Dale, Apr 18 2016

G.f.: (1 + 19*x + 75*x^2 + 85*x^3 + 28*x^4 + 2*x^5) / (1 - x)^10. - Colin Barker, Apr 22 2020

Maple

a:=n->(1/8640)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(5*n^2+23*n+30): seq(a(n), n=0..26);

Mathematica

Table[(n+1)(n+2)^3(n+3)^2(n+4)(5n^2+23n+30)/8640, {n, 0, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 29, 320, 2100, 9898, 37044, 116928, 323730, 807675, 1851421}, 30] (* Harvey P. Dale, Apr 18 2016 *)

Prog

(PARI) Vec((1 + 19*x + 75*x^2 + 85*x^3 + 28*x^4 + 2*x^5) / (1 - x)^10 + O(x^30)) \\ Colin Barker, Apr 22 2020

Crossrefs

Sequence in context: A165616 A142380 A042632 * A057131 A160442 A125417

Adjacent sequences: A107963 A107964 A107965 * A107967 A107968 A107969

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved