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. 229).
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 + 13*x + 28*x^2 + 13*x^3 + 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)
Sum_{n>=0} 1/a(n) = 120*Pi^2 - 144*sqrt(5)*Pi*tan(sqrt(5)*Pi/2) - 790. - Amiram Eldar, May 31 2022
MAPLE
a:=n->(1/720)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2+5*n+5): seq(a(n), n=0..30);
MATHEMATICA
Table[(n+1)(n+2)^2(n+3)^2(n+4)(n^2+5n+5)/720, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835}, 30] (* Harvey P. Dale, Sep 27 2020 *)
PROG
(PARI) Vec((1 + 13*x + 28*x^2 + 13*x^3 + x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
editing