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.233, # 10).
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: (1 + 8*x + 9*x^2 + x^3)/(1-x)^7.
MAPLE
a:=n->(n+1)*(n+2)*(n+3)*(19*n^3+111*n^2+200*n+120)/720: seq(a(n), n=0..33);
MATHEMATICA
Table[(n + 1) (n + 2) (n + 3) (19 n^3 + 111 n^2 + 200 n + 120)/720, {n, 0, 29}] (* or *)
CoefficientList[Series[(1 + 8 x + 9 x^2 + x^3)/(1 - x)^7, {x, 0, 29}], x] (* or *)
Table[Sum[Binomial[(n + 1 - k) + 1, 2] Apply[Subtract, Map[Binomial[# + 2, 3] &, {n + 1, k}]], {k, 0, n}], {n, 0, 29}] (* Michael De Vlieger, Jun 08 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved