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A193075 Decimal expansion of the constant term of the reduction of t^x by x^2->x+1, where t=(1+sqrt(5))/2, the golden ratio. 3
1, 1, 3, 9, 5, 6, 4, 7, 0, 6, 8, 7, 9, 3, 2, 1, 6, 0, 8, 2, 3, 7, 8, 8, 1, 6, 5, 0, 5, 7, 9, 3, 1, 8, 7, 1, 1, 3, 1, 7, 3, 5, 8, 0, 0, 7, 5, 5, 8, 5, 2, 2, 8, 1, 7, 4, 5, 0, 1, 3, 3, 5, 1, 7, 8, 9, 0, 7, 2, 4, 8, 6, 0, 3, 9, 5, 9, 6, 7, 2, 5, 7, 3, 4, 6, 3, 0, 2, 0, 5, 5, 2, 9, 8, 2, 5, 0, 2, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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=1..100.

EXAMPLE

constant=1.13956470687932160823788165057931871131735800...

MATHEMATICA

t = GoldenRatio

f[x_] := t^(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]  (* A193075 *)

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

RealDigits[u1, 10]  (* A193076 *)

CROSSREFS

Cf. A193010, A192232, A193076.

Sequence in context: A085851 A212321 A092041 * A106586 A010633 A199053

Adjacent sequences:  A193072 A193073 A193074 * A193076 A193077 A193078

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jul 15 2011

STATUS

approved

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Last modified October 30 13:31 EDT 2014. Contains 248803 sequences.