A192302 0-sequence of reduction of the upper Wythoff sequence by x^2 -> x+1.

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

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