A193034 - OEIS

A193034

Decimal expansion of the coefficient of x in the reduction of 3^x by x^2->x+1.

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

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OFFSET

1,1

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 Sum_{k>=0} log(3)^k*Fibonacci(k)/k!.

Equals (3^sqrt(5)-1)/(sqrt(5)*3^(phi-1)), where phi is the golden ratio (A001622). (End)

EXAMPLE