cp's OEIS Frontend

A193012 Decimal expansion of the coefficient of x in the reduction of sin(x) by x^2->x+1.

%I A193012 #18 Jan 18 2022 02:27:52
%S A193012 7,0,5,8,4,5,4,7,0,4,5,7,2,3,4,3,9,3,7,3,7,8,0,8,7,5,3,5,0,2,0,3,9,3,
%T A193012 8,7,5,3,0,4,3,1,8,8,8,8,8,7,3,4,5,0,0,1,8,4,7,1,7,3,7,3,9,7,9,6,7,2,
%U A193012 0,9,7,7,0,0,2,2,9,0,3,5,1,3,1,6,4,6,9,6,1,8,8,3,1,6,8,5,4,1,3,3
%N A193012 Decimal expansion of the coefficient of x in the reduction of sin(x) by x^2->x+1.
%C A193012 Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.
%F A193012 From _Amiram Eldar_, Jan 18 2022: (Start)
%F A193012 Equals Sum_{k>=0} (-1)^k*Fibonacci(2*k+1)/(2*k+1)!.
%F A193012 Equals 2*cos(1/2)*sin(sqrt(5)/2)/sqrt(5). (End)
%e A193012 0.705845470457234393737808753502039387530431888887345001...
%t A193012 f[x_] := Sin[x]; r[n_] := Fibonacci[n];
%t A193012 c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
%t A193012 u1 = N[Sum[c[n]*r[n], {n, 0, 200}], 100]
%t A193012 RealDigits[u1, 10]
%Y A193012 Cf. A000045, A193010, A193011, A192232.
%K A193012 nonn,cons
%O A193012 0,1
%A A193012 _Clark Kimberling_, Jul 14 2011