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

1,1

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}).

Links

Table of n, a(n) for n=1..17.

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

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);

Crossrefs

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

Sequence in context: A296660 A197898 A293471 * A099976 A195157 A207151

Adjacent sequences: A109103 A109104 A109105 * A109107 A109108 A109109

Keyword

nonn

Author

Emeric Deutsch, Jun 19 2005

Status

approved