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.
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)
EXAMPLE
-0.29606728112980805107973977013969639291652...
MATHEMATICA
f[x_] := Cos[x]^2; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
RealDigits[u1, 10]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 15 2011
STATUS
approved