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A193087 Decimal expansion of the constant term of the reduction of (cos(x))^2 by x^2->x+1. 3
4, 8, 1, 2, 7, 6, 6, 6, 1, 3, 1, 5, 0, 7, 0, 8, 0, 3, 0, 0, 6, 9, 7, 2, 2, 2, 2, 9, 6, 1, 1, 3, 4, 3, 9, 6, 9, 5, 8, 4, 7, 1, 5, 9, 4, 6, 4, 5, 7, 5, 4, 6, 2, 0, 7, 2, 7, 6, 6, 6, 3, 0, 6, 2, 5, 3, 0, 0, 2, 7, 9, 3, 1, 2, 4, 7, 4, 4, 3, 9, 1, 6, 8, 7, 1, 7, 8, 9, 4, 4, 7, 5, 9, 8, 6, 8, 4, 5, 3, 0 (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.

LINKS

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

EXAMPLE

constant=0.48127666131507080300697222296113439695...

MATHEMATICA

f[x_] := Cos[x]^2; r[n_] := Fibonacci[n];

c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]

u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100]

RealDigits[u0, 10]  (* A193087 *)

u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]

RealDigits[u1, 10]  (* A193088 *)

CROSSREFS

Cf. A193010, A192232, A193088.

Sequence in context: A154520 A244690 A002390 * A201404 A122149 A254149

Adjacent sequences:  A193084 A193085 A193086 * A193088 A193089 A193090

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jul 15 2011

STATUS

approved

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Last modified February 20 12:33 EST 2018. Contains 299379 sequences. (Running on oeis4.)