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%I #9 Mar 03 2024 12:45:17
%S 1,1,5,11,27,54,109,205,387,723,1301,2346,4215,7383,12975,22400,38870,
%T 67493,115403,198091,336064,572839,977841,1650859,2797139,4744595,
%U 7970670,13433355,22468583,37723511,63434961,105869001,177221258,297028253,494404621,825172067
%N 0-sequence of reduction of the lower Wythoff sequence by x^2 -> x+1.
%C See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%t c[n_] := Floor[n*GoldenRatio]; (* Lower Wythoff sequence, A000201 *)
%t Table[c[n], {n, 1, 15}]
%t q[x_] := x + 1;
%t p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
%t reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
%t x^y_?OddQ -> x q[x]^((y - 1)/2)};
%t t = Table[
%t Last[Most[
%t FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
%t 30}]
%t Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}] (* A192300 *)
%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192301 *)
%t (* by _Peter J. C. Moses_, Jun 20 2011 *)
%Y Cf. A192232, A192301.
%K nonn
%O 1,3
%A _Clark Kimberling_, Jun 27 2011
%E a(31)-a(36) (using the Mathematica code) from _Pontus von Brömssen_, Mar 03 2024
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