OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
First differences of A114242. - Peter Bala, Sep 21 2007
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 167-169, Table 10.5/II/5).
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: (1+x)(1 + 5x + x^2)/(1-x)^7.
From Amiram Eldar, May 31 2022: (Start)
Sum_{n>=0} 1/a(n) = 5*Pi*(7*sqrt(14)*coth(sqrt(2/7)*Pi) - 6*Pi) - 1295/9.
Sum_{n>=0} (-1)^n/a(n) = 5*Pi*(7*sqrt(14)*cosech(sqrt(2/7)*Pi) + 3*Pi) - 2755/9. (End)
MAPLE
a:=n->(n+1)*(n+2)^2*(n+3)*(7*n^2+28*n+30)/360: seq(a(n), n=0..35);
MATHEMATICA
Table[(n + 1)*(n + 2)^2*(n + 3)*(7*n^2 + 28*n + 30)/360, {n, 0, 30}] (* Amiram Eldar, May 31 2022 *)
CoefficientList[Series[(1+x)(1+5x+x^2)/(1-x)^7, {x, 0, 40}], x] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {1, 13, 76, 295, 889, 2254, 5040}, 40] (* Harvey P. Dale, Mar 06 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 18 2005
STATUS
approved