cp's OEIS Frontend

A193011 Decimal expansion of the constant term of the reduction of sin(x) by x^2->x+1.

%I A193011 #14 Jan 18 2022 02:31:44
%S A193011 1,4,3,1,9,7,4,5,2,9,1,0,0,8,0,2,3,2,6,4,1,5,0,3,6,4,7,7,2,4,6,4,1,0,
%T A193011 8,4,9,9,0,8,8,9,2,8,6,2,3,8,9,1,3,5,5,1,7,4,6,3,3,8,8,6,4,3,3,5,0,1,
%U A193011 0,7,1,2,6,6,1,3,3,6,4,0,8,9,0,9,5,6,1,9,7,3,1,0,8,5,2,8,5,9,1,0
%N A193011 Decimal expansion of the constant term of the reduction of sin(x) by x^2->x+1.
%C A193011 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193011 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193011 Equals Sum_{k>=1} (-1)^k*Fibonacci(2*k)/(2*k+1)!.
%F A193011 Equals cos(sqrt(5)/2)*sin(1/2) - cos(1/2)*sin(sqrt(5)/2)/sqrt(5). (End)
%e A193011 -0.143197452910080232641503647724641084990...
%t A193011 f[x_] := Sin[x]; r[n_] := Fibonacci[n];
%t A193011 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193011 u0 = N[Sum[c[n]*r[n - 1], {n, 0, 200}], 100]
%t A193011 RealDigits[u0, 10]
%Y A193011 Cf. A000045, A193010, A192232, A193012.
%K A193011 nonn,cons
%O A193011 0,2
%A A193011 _Clark Kimberling_, Jul 14 2011