A109106 a(n) = (1/sqrt(5))*((sqrt(5) + 1)*((15 + 5*sqrt(5))/2)^(n-1) + (sqrt(5) - 1)*((15 - 5*sqrt(5))/2)^(n-1)).

2, 20, 250, 3250, 42500, 556250, 7281250, 95312500, 1247656250, 16332031250, 213789062500, 2798535156250, 36633300781250, 479536132812500, 6277209472656250, 82169738769531250, 1075615844726562500

Offset: 1

Author

Emeric Deutsch, Jun 19 2005

Keywords

• nonn

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. 215, K{T_m}).

Crossrefs

Cf. A179135. - Johannes W. Meijer, Jul 01 2010

Programs

Maple

a:=n->(1/sqrt(5))*((sqrt(5)+1)*((15+5*sqrt(5))/2)^(n-1)+(sqrt(5)-1)*((15-5*sqrt(5))/2)^(n-1)): seq(expand(a(n)),n=1..19);

Formula

G.f.: 2z(1-5z)/(1 - 15z + 25z^2).

From Johannes W. Meijer, Jul 01 2010: (Start)

a(n) = A178381(4*n+2).

Lim_{k->infinity} a(n+k)/a(k) = (A020876(2*n) + 5*A039717(2*n-2)*sqrt(5))/2.

Lim_{n->infinity} A020876(2*n)/(5*A039717(2*n-2)) = sqrt(5).

(End)

a(n) = 2*5^(n-1)*Fibonacci(2*n-1). - Ehren Metcalfe, Apr 21 2018