OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids. - Emeric Deutsch, Oct 16 2006
Form the 2 X 3 matrix with first row C(n,0), C(n,1), and C(n,2) and second row C(n+1,0), C(n+1,1), and C(n+1,2), multiply it by its transpose to get a 2 X 2 matrix: its determinant = a(n). - J. M. Bergot, Sep 05 2013
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 120).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (-1 + 2*x - 9*x^2 + 4*x^3 - 2*x^4) / (x-1)^5 . - R. J. Mathar, Oct 19 2012
a(n) = 1 + A117717(n+1). - R. J. Mathar, Sep 15 2013
E.g.f.: (x^4 + 8*x^3 + 18*x^2 + 8*x + 4)*exp(x)/4. - G. C. Greubel, Oct 12 2017
MAPLE
a:=n->(n^4+2*n^3+5*n^2+4)/4: seq(a(n), n=0..40); # Emeric Deutsch, Oct 16 2006
MATHEMATICA
Table[(n^4 + 2*n^3 + 5*n^2 + 4)/4, {n, 0, 50}] (* G. C. Greubel, Oct 12 2017 *)
PROG
(PARI) for(n=0, 50, print1((n^4 + 2*n^3 + 5*n^2 + 4)/4, ", ")) \\ G. C. Greubel, Oct 12 2017
(Magma) [(n^4 + 2*n^3 + 5*n^2 + 4)/4: n in [0..30]]; // G. C. Greubel, Oct 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 10 2006
EXTENSIONS
More terms from Emeric Deutsch, Oct 16 2006
STATUS
approved