OFFSET
1,1
COMMENTS
Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
FORMULA
From Amiram Eldar, Jan 19 2022: (Start)
Equals 1 + Sum_{k>=1} log(3)^k*Fibonacci(k-1)/k!.
Equals (9^phi + 3*phi^2)/(sqrt(5)*phi*3^phi), where phi is the golden ratio (A001622). (End)
EXAMPLE
2.00199585716593447105854181212612374067547375969106000...
MATHEMATICA
f[x_] := 3^x; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
RealDigits[u0, 10]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 14 2011
STATUS
approved