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A192302 0-sequence of reduction of the upper Wythoff sequence by x^2 -> x+1. 2
2, 2, 9, 19, 45, 90, 180, 340, 639, 1185, 2137, 3842, 6868, 12052, 21139, 36596, 63436, 109825, 188078, 322446, 548220, 933825, 1590585, 2688667, 4551372, 7704396, 12956146, 21817835, 36549185, 61338443 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

LINKS

Table of n, a(n) for n=1..30.

MATHEMATICA

c[n_] :=

n + Floor[n*GoldenRatio]; (* Upper Wythoff sequence, A001950 *)

Table[c[n], {n, 1, 15}]

q[x_] := x + 1;

p[0, x_] := 2; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]

reductionRules = {x^y_?EvenQ -> q[x]^(y/2),

   x^y_?OddQ -> x q[x]^((y - 1)/2)};

t = Table[

  Last[Most[

    FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,

   30}]

Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192302 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192303 *)

(* by Peter J. C. Moses, Jun 20 2011 *)

CROSSREFS

Cf. A192232, A192303.

Sequence in context: A224244 A007024 A019223 * A128535 A180753 A220971

Adjacent sequences:  A192299 A192300 A192301 * A192303 A192304 A192305

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 27 2011

STATUS

approved

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Last modified August 1 21:02 EDT 2021. Contains 346408 sequences. (Running on oeis4.)