A135422 a(1) = 1, a(n) = Sum(k=1,n-1, a(k)^F(n-k)) where F(m) is the m-th Fibonacci number.

1, 1, 2, 4, 8, 18, 52, 232, 2402, 117668, 88187304, 4976488920530, 304428188114211553556, 1303145665493529877195427353444744, 383170653295945759116409236671895695428812677131461090

Offset

1,3

Comments

Conjecture: limit n->infinity Phi^(Phi^(n-c))/a(n) = 1 where c is a constant = 3.47348961175710091....

Links

G. C. Greubel, Table of n, a(n) for n = 1..20

Mathematica

a[1]:= 1; a[n_] := Sum[a[k]^Fibonacci[n - k], {k, 1, n - 1}]; Join[{1}, Table[a[n], {n, 2, 10}]] (* G. C. Greubel, Oct 13 2016 *)

Prog

(PARI) a=vector(16); a[1]=1; print1("1, "); for(n=2, 16, a[n]=sum(k=1, n-1, a[k]^fibonacci(n-k)); print1(a[n], ", "))

Crossrefs

Cf. A000045, A001622.

Sequence in context: A333497 A367115 A166952 * A116723 A323020 A180206

Adjacent sequences: A135419 A135420 A135421 * A135423 A135424 A135425

Keyword

nonn

Author

Gerald McGarvey, Dec 12 2007

Status

approved