A107967 a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(n^2 + 4n + 5)/1440.

1, 30, 340, 2275, 10878, 41160, 131040, 365310, 916575, 2110966, 4528524, 9150505, 17568460, 32272800, 57041664, 97454268, 161556525, 260710590, 410664100, 632879247, 956166442, 1418672200, 2070276000, 2975456250, 4216691115

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

Formula

From Colin Barker, Apr 22 2020: (Start)

G.f.: (1 + 20*x + 85*x^2 + 105*x^3 + 38*x^4 + 3*x^5) / (1 - x)^10.

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) for n>9.

(End)

Maple

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

Prog

(PARI) Vec((1 + 20*x + 85*x^2 + 105*x^3 + 38*x^4 + 3*x^5) / (1 - x)^10 + O(x^30)) \\ Colin Barker, Apr 22 2020

Crossrefs

Sequence in context: A227689 A006859 A341557 * A354656 A115500 A214085

Adjacent sequences: A107964 A107965 A107966 * A107968 A107969 A107970

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 12 2005

Status

approved