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A108671
a(n) = (n+1)(n+2)^3*(n+3)(13n^2 + 37n + 30)/720.
1
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).
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 17 2005
STATUS
approved