A193088 - OEIS

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A193088

Decimal expansion of the coefficient of x in the reduction of (cos(x))^2 by x^2->x+1 (negated).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

The positive value +0.2960... is the coefficient of x in the reduction of (sin(x))^2 by x^2->x+1.

LINKS

Table of n, a(n) for n=0..99.

FORMULA

From Amiram Eldar, Jan 19 2022: (Start)

Equals Sum_{k>=0} (-1)^k * 2^(2*k-1) * Fibonacci(2*k)/(2*k)!.

Equals -sin(1)*sin(sqrt(5))/sqrt(5). (End)