OFFSET
0,1
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. 311).
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: 16*(27 + 403*x + 473*x^2 - 15*x^3 + 14*x^4 - 2*x^5)/(1-x)^7.
From Amiram Eldar, Jun 02 2022: (Start)
Sum_{n>=0} 1/a(n) = 197/864 - Pi^2/144 - (5/144)*sqrt(5/2)*Pi*cot(2*sqrt(2/5)*Pi).
Sum_{n>=0} (-1)^n/a(n) = -85/432 - Pi^2/288 - (5/144)*sqrt(5/2)*Pi*cosec(2*sqrt(2/5)*Pi). (End)
MAPLE
a:=n->4*(n+1)^2*(n+3)^2*(5*n^2+20*n+12): seq(a(n), n=0..28);
MATHEMATICA
Table[4*(n + 1)^2*(n + 3)^2*(5*n^2 + 20*n + 12), {n, 0, 30}] (* Amiram Eldar, Jun 02 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved