A192300 0-sequence of reduction of the lower Wythoff sequence by x^2 -> x+1.

1, 1, 5, 11, 27, 54, 109, 205, 387, 723, 1301, 2346, 4215, 7383, 12975, 22400, 38870, 67493, 115403, 198091, 336064, 572839, 977841, 1650859, 2797139, 4744595, 7970670, 13433355, 22468583, 37723511, 63434961, 105869001, 177221258, 297028253, 494404621, 825172067

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..36.

Mathematica

c[n_] := Floor[n*GoldenRatio]; (* Lower Wythoff sequence, A000201 *)
Table[c[n], {n, 1, 15}]
q[x_] := x + 1;
p[0, x_] := 1; 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}]  (* A192300 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192301 *)
(* by Peter J. C. Moses, Jun 20 2011 *)

Crossrefs

Cf. A192232, A192301.

Sequence in context: A042423 A356351 A206440 * A289775 A119503 A048655

Adjacent sequences: A192297 A192298 A192299 * A192301 A192302 A192303

Keyword

nonn

Author

Clark Kimberling, Jun 27 2011

Extensions

a(31)-a(36) (using the Mathematica code) from Pontus von Brömssen, Mar 03 2024

Status

approved