cp's OEIS Frontend

A193033 Decimal expansion of the constant term of the reduction of 3^x by x^2->x+1.

%I A193033 #10 Jan 19 2022 04:56:30
%S A193033 2,0,0,1,9,9,5,8,5,7,1,6,5,9,3,4,4,7,1,0,5,8,5,4,1,8,1,2,1,2,6,1,2,3,
%T A193033 7,4,0,6,7,5,4,7,3,7,5,9,6,9,1,0,6,0,0,0,1,0,1,9,6,4,0,0,9,4,1,9,2,9,
%U A193033 6,7,8,9,1,5,5,1,7,3,4,7,7,1,3,6,0,1,2,6,9,0,8,9,4,2,4,8,9,5,2,3
%N A193033 Decimal expansion of the constant term of the reduction of 3^x by x^2->x+1.
%C A193033 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193033 From _Amiram Eldar_, Jan 19 2022: (Start)
%F A193033 Equals 1 + Sum_{k>=1} log(3)^k*Fibonacci(k-1)/k!.
%F A193033 Equals (9^phi + 3*phi^2)/(sqrt(5)*phi*3^phi), where phi is the golden ratio (A001622). (End)
%e A193033 2.00199585716593447105854181212612374067547375969106000...
%t A193033 f[x_] := 3^x; r[n_] := Fibonacci[n];
%t A193033 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193033 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]
%t A193033 RealDigits[u0, 10]
%Y A193033 Cf. A000045, A001622, A193010, A192232, A193034.
%K A193033 nonn,cons
%O A193033 1,1
%A A193033 _Clark Kimberling_, Jul 14 2011