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A192254 0-sequence of reduction of (n^2) by x^2 -> x+1. 3
1, 1, 10, 26, 76, 184, 429, 941, 1994, 4094, 8208, 16128, 31169, 59393, 111818, 208330, 384620, 704408, 1280925, 2314525, 4158346, 7432606, 13223040, 23424576, 41335201, 72679969, 127373194, 222545306, 387732844, 673762744 (list; graph; refs; listen; history; text; internal format)
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..30.

FORMULA

Empirical G.f.: x*(1-3*x+9*x^2-6*x^3+2*x^4)/(1-x)/(1-x-x^2)^3. [Colin Barker, Feb 10 2012]

MATHEMATICA

c[n_] := n^2;  (* A000290 *)

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}]  (* A192254 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]   (* A192255 *)

(* by Peter J. C. Moses, Jun 20 2011 *)

CROSSREFS

Sequence in context: A259290 A072379 A005970 * A220155 A321311 A051966

Adjacent sequences:  A192251 A192252 A192253 * A192255 A192256 A192257

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 27 2011

STATUS

approved

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Last modified February 17 00:25 EST 2020. Contains 331976 sequences. (Running on oeis4.)