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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)).
4
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}).
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved