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A307082 Expansion of 1/(1 - x/(1 - x/(1 - 2*x/(1 - 3*x/(1 - 5*x/(1 - 8*x/(1 - ... - Fibonacci(k)*x/(1 - ...)))))))), a continued fraction. 3
1, 1, 2, 6, 26, 164, 1540, 22068, 492616, 17378968, 977896328, 88256247312, 12819022165520, 3002745820555664, 1135759674922075168, 694219521332053782624, 686053892556368634929824, 1096476587053610841771551296, 2834651494015025836540377942080 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * phi^(n*(n+1)/2) / 5^(n/2), where phi = A001622 is the golden ratio and c = 10.15498753508843821457456033641336796744756370048241257586748102558791... - Vaclav Kotesovec, Sep 18 2021
MAPLE
b:= proc(x, y) option remember; (F->
`if`(x=0 and y=0, 1, `if`(x>0, b(x-1, y)*F(y-x+1), 0)+
`if`(y>x, b(x, y-1), 0)))(combinat[fibonacci])
end:
a:= n-> b(n$2):
seq(a(n), n=0..18); # Alois P. Heinz, Nov 12 2023
MATHEMATICA
nmax = 18; CoefficientList[Series[1/(1 + ContinuedFractionK[-Fibonacci[k] x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A180349 A141713 A005272 * A178089 A363003 A002449
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 23 2019
STATUS
approved

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Last modified March 2 15:05 EST 2024. Contains 370494 sequences. (Running on oeis4.)