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A193083 Decimal expansion of the constant term of the reduction of (e^x)*cos(x) by x^2->x+1. 3
2, 5, 2, 0, 5, 8, 9, 8, 4, 0, 6, 6, 7, 7, 5, 3, 6, 2, 7, 4, 2, 5, 8, 4, 7, 7, 8, 2, 5, 2, 4, 7, 8, 2, 9, 4, 3, 6, 5, 9, 0, 9, 7, 1, 1, 8, 9, 8, 5, 9, 3, 9, 3, 2, 8, 1, 9, 7, 8, 4, 2, 6, 4, 8, 5, 2, 3, 1, 6, 8, 8, 8, 4, 8, 6, 2, 8, 1, 9, 2, 3, 3, 5, 3, 8, 7, 9, 8, 3, 3, 1, 7, 6, 1, 6, 8, 7, 5, 2, 1 (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=0.25205898406677536274258477825247829436590...

MATHEMATICA

f[x_] := Exp[x] Cos[x]; 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]  (* A193083 *)

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

RealDigits[u1, 10]  (* A193084 *)

CROSSREFS

Cf. A193010, A192232, A193084.

Sequence in context: A190950 A159985 A259667 * A146103 A245172 A196527

Adjacent sequences:  A193080 A193081 A193082 * A193084 A193085 A193086

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jul 15 2011

STATUS

approved

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Last modified October 15 22:14 EDT 2018. Contains 316237 sequences. (Running on oeis4.)