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. 168).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Chai Wah Wu, Nov 11 2018: (Start)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.
G.f.: (4*x^2 + 6*x + 1)/(x - 1)^6. (End)
E.g.f.: (120 + 1320*x + 2280*x^2 + 1160*x^3 + 205*x^4 + 11*x^5)*exp(x)/5!. - G. C. Greubel, Nov 11 2018
MAPLE
a:=n->(n+1)*(n+2)*(n+3)*(11*n^2+29*n+20)/120: seq(a(n), n=0..38);
MATHEMATICA
Table[Binomial[n+3, 3]*(11*n^2 +29*n +20)/20, {n, 0, 20}] (* G. C. Greubel, Nov 11 2018 *)
PROG
(PARI) vector(35, n, n--; binomial(n+3, 3)*(11*n^2 +29*n +20)/20) \\ G. C. Greubel, Nov 11 2018
(Magma) [Binomial(n+3, 3)*(11*n^2 +29*n +20)/20: n in [0..35]]; // G. C. Greubel, Nov 11 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 18 2005
STATUS
approved