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A192254 0-sequence of reduction of (n^2) by x^2 -> x+1. 3

%I

%S 1,1,10,26,76,184,429,941,1994,4094,8208,16128,31169,59393,111818,

%T 208330,384620,704408,1280925,2314525,4158346,7432606,13223040,

%U 23424576,41335201,72679969,127373194,222545306,387732844,673762744

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

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

%F 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]

%t c[n_] := n^2; (* A000290 *)

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

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

%t p[0, x_] := 1; 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}] (* A192254 *)

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

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

%K nonn

%O 1,3

%A _Clark Kimberling_, Jun 27 2011

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Last modified April 6 08:44 EDT 2020. Contains 333268 sequences. (Running on oeis4.)