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A108684
a(n) = (n+1)*(n+2)*(n+3)*(19*n^3 + 111*n^2 + 200*n + 120)/720.
0
1, 15, 93, 372, 1141, 2926, 6594, 13476, 25509, 45397, 76791, 124488, 194649, 295036, 435268, 627096, 884697, 1224987, 1667953, 2237004, 2959341, 3866346, 4993990, 6383260, 8080605, 10138401, 12615435, 15577408, 19097457, 23256696
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.233, # 10).
FORMULA
G.f.: (1 + 8*x + 9*x^2 + x^3)/(1-x)^7.
a(n) = Sum_{k=0...n} A000217(n+1-k) * (A000292(n+1) - A000292(k)). - J. M. Bergot, Jun 07 2017
a(n) = A050405(n) + A181888(n+1). - R. J. Mathar, Jul 22 2022
MAPLE
a:=n->(n+1)*(n+2)*(n+3)*(19*n^3+111*n^2+200*n+120)/720: seq(a(n), n=0..33);
MATHEMATICA
Table[(n + 1) (n + 2) (n + 3) (19 n^3 + 111 n^2 + 200 n + 120)/720, {n, 0, 29}] (* or *)
CoefficientList[Series[(1 + 8 x + 9 x^2 + x^3)/(1 - x)^7, {x, 0, 29}], x] (* or *)
Table[Sum[Binomial[(n + 1 - k) + 1, 2] Apply[Subtract, Map[Binomial[# + 2, 3] &, {n + 1, k}]], {k, 0, n}], {n, 0, 29}] (* Michael De Vlieger, Jun 08 2017 *)
CROSSREFS
Sequence in context: A329759 A041428 A052226 * A125325 A126483 A226766
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved