A193075 - OEIS

A193075

Decimal expansion of the constant term of the reduction of phi^x by x^2->x+1, where phi=(1+sqrt(5))/2 is the golden ratio (A001622).

1, 1, 3, 9, 5, 6, 4, 7, 0, 6, 8, 7, 9, 3, 2, 1, 6, 0, 8, 2, 3, 7, 8, 8, 1, 6, 5, 0, 5, 7, 9, 3, 1, 8, 7, 1, 1, 3, 1, 7, 3, 5, 8, 0, 0, 7, 5, 5, 8, 5, 2, 2, 8, 1, 7, 4, 5, 0, 1, 3, 3, 5, 1, 7, 8, 9, 0, 7, 2, 4, 8, 6, 0, 3, 9, 5, 9, 6, 7, 2, 5, 7, 3, 4, 6, 3, 0, 2, 0, 5, 5, 2, 9, 8, 2, 5, 0, 2, 2, 0

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OFFSET

1,3

COMMENTS

Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.

LINKS

Table of n, a(n) for n=1..100.

FORMULA

From Amiram Eldar, Jan 19 2022: (Start)

Equals 1 + Sum_{k>=1} log(phi)^k*Fibonacci(k-1)/k!.

Equals (sqrt(5)*phi^sqrt(5) + phi^4 - 1)/(5*phi^phi). (End)

EXAMPLE