A192302 - OEIS

%I #5 Dec 04 2016 19:46:25

%S 2,2,9,19,45,90,180,340,639,1185,2137,3842,6868,12052,21139,36596,

%T 63436,109825,188078,322446,548220,933825,1590585,2688667,4551372,

%U 7704396,12956146,21817835,36549185,61338443

%N 0-sequence of reduction of the upper Wythoff sequence by x^2 -> x+1.

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

%t c[n_] :=

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

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

%t q[x_] := x + 1;

%t p[0, x_] := 2; 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}]  (* A192302 *)

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

%t (* by _Peter J. C. Moses_, Jun 20 2011 *)

%Y Cf. A192232, A192303.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jun 27 2011