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A114480
Kekulé numbers for certain benzenoids.
0
4, 50, 650, 8500, 111250, 1456250, 19062500, 249531250, 3266406250, 42757812500, 559707031250, 7326660156250, 95907226562500, 1255441894531250, 16433947753906250, 215123168945312500, 2815998840332031250
OFFSET
1,1
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 205).
FORMULA
a(n) = 2*((sqrt(5) + 2)((15 + 5*sqrt(5))/2)^(n-1) + (sqrt(5) - 2)*((15 - 5*sqrt(5))/2)^(n-1))/sqrt(5).
From Colin Barker, Aug 30 2013: (Start)
a(n) = 15*a(n-1) - 25*a(n-2).
G.f.: -2*x*(5*x-2) / (25*x^2 - 15*x + 1). (End)
MAPLE
a:=2*((sqrt(5)+2)*((15+5*sqrt(5))/2)^(n-1)+(sqrt(5)-2)*((15-5*sqrt(5))/2)^(n-1))/sqrt(5): seq(expand(a(n)), n=1..20);
MATHEMATICA
LinearRecurrence[{15, -25}, {4, 50}, 20] (* Harvey P. Dale, Oct 01 2023 *)
CROSSREFS
Sequence in context: A232731 A215792 A280358 * A123356 A234870 A139087
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 30 2005
STATUS
approved