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A108178 a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(7n^2 + 23n + 20)/2880. 1
1, 25, 235, 1330, 5488, 18228, 51660, 129690, 295845, 624481, 1236235, 2318680, 4153240, 7149520, 11888304, 19174572, 30101985, 46130385, 69177955, 101729782, 146964664, 208902100, 292571500, 404205750, 551461365, 743667561, 992106675 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
LINKS
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230, no. 20).
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
From Colin Barker, Apr 22 2020: (Start)
G.f.: (1 + 16*x + 46*x^2 + 31*x^3 + 4*x^4) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
(End)
MAPLE
a:=(n+1)*(n+2)^2*(n+3)^2*(n+4)*(7*n^2+23*n+20)/2880: seq(a(n), n=0..30);
MATHEMATICA
Table[(n+1)(n+2)^2(n+3)^2(n+4)(7n^2+23n+20)/2880, {n, 0, 50}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 25, 235, 1330, 5488, 18228, 51660, 129690, 295845}, 50] (* Harvey P. Dale, Aug 16 2021 *)
PROG
(PARI) Vec((1 + 16*x + 46*x^2 + 31*x^3 + 4*x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020
CROSSREFS
Sequence in context: A221930 A160222 A088890 * A278849 A294290 A352304
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 13 2005
STATUS
approved

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Last modified April 16 18:22 EDT 2024. Contains 371750 sequences. (Running on oeis4.)