A108671 a(n) = (n+1)(n+2)^3*(n+3)(13n^2 + 37n + 30)/720.

1, 24, 208, 1075, 4053, 12348, 32256, 75006, 159225, 314116, 583440, 1030393, 1743469, 2843400, 4491264, 6897852, 10334385, 15144672, 21758800, 30708447, 42643909, 58352932, 78781440, 105056250, 138509865, 180707436, 233475984

Offset

0,2

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. 231, # 29).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

From Colin Barker, Apr 23 2020: (Start)

G.f.: (1 + 16*x + 44*x^2 + 27*x^3 + 3*x^4) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

(End)

Maple

a:=n->(n+1)*(n+2)^3*(n+3)*(13*n^2+37*n+30)/720: seq(a(n), n=0..32);

Prog

(PARI) Vec((1 + 16*x + 44*x^2 + 27*x^3 + 3*x^4) / (1 - x)^8 + O(x^30)) \\ Colin Barker, Apr 23 2020

Crossrefs

Sequence in context: A282644 A283540 A047659 * A097321 A105946 A050222

Adjacent sequences: A108668 A108669 A108670 * A108672 A108673 A108674

Keyword

nonn,easy

Author

Emeric Deutsch, Jun 17 2005

Status

approved