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. 232, # 4).
LINKS
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: (1+x)*(1+6*x)/(1-x)^8.
From Amiram Eldar, Jun 02 2022: (Start)
Sum_{n>=0} 1/a(n) = 20*Pi^2 - 3072*log(2)/7 + 4531/42.
Sum_{n>=0} (-1)^n/a(n) = 768*Pi/7 - 10*Pi^2 - 256*log(2)/7 - 9227/42. (End)
MAPLE
G:=factor(sum(a(n)*z^n, n=0..infinity)); series(G, z=0, 37);
MATHEMATICA
Table[(n+1)(n+2)^2(n+3)(n+4)(n+5)(2n+3)/720, {n, 0, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 15, 98, 420, 1386, 3822, 9240, 20196}, 30] (* Harvey P. Dale, Sep 23 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 18 2005
STATUS
approved