A192305 0-sequence of reduction of (2n) by x^2 -> x+1.

2, 2, 8, 16, 36, 72, 142, 270, 504, 924, 1672, 2992, 5306, 9338, 16328, 28392, 49132, 84664, 145350, 248710, 424312, 721972, 1225488, 2075616, 3508466, 5919602, 9970952, 16768960, 28161204, 47229864, 79112062, 132362622, 221216376, 369341388, 616061848, 1026669712, 1709502122, 2844208874, 4728518600, 7855572120

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..40.

Formula

a(n) = 2*A190062(n).

G.f.: 2*x*(1-2*x+2*x^2)/((1-x)*(1-x-x^2)^2). [Colin Barker, Feb 11 2012]

Mathematica

c[n_] := 2 n; (* even numbers, A005843 *)
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,
   40}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 40}]  (* A192305  *)
Table[Coefficient[Part[t, n]/2, x, 0], {n, 1, 40}]  (* A190062 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 40}]  (* A192306 *)
Table[Coefficient[Part[t, n]/2, x, 1], {n, 1, 40}]  (* A122491 *)
(* by Peter J. C. Moses, Jun 20 2011 *)

Crossrefs

Cf. A192232, A192306, A192304.

Sequence in context: A361294 A220172 A276054 * A228797 A052970 A220589

Adjacent sequences: A192302 A192303 A192304 * A192306 A192307 A192308

Keyword

nonn,easy

Author

Clark Kimberling, Jun 27 2011

Status

approved