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A192302
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0-sequence of reduction of the upper Wythoff sequence by x^2 -> x+1.
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2
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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
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OFFSET
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1,1
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COMMENTS
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See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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