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, 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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 13 2005
STATUS
approved