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

%I #8 Dec 04 2016 19:46:25

%S 1,1,8,18,44,92,187,363,688,1276,2330,4200,7493,13253,23272,40614,

%T 70504,121828,209663,359535,614576,1047536,1780918,3020688,5112649,

%U 8636617,14563592,24517818,41213348,69180716

%N 0-sequence of reduction of (3n-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*(1-2*x+6*x^2-2*x^3)/(1-3*x+x^2+3*x^3-x^4-x^5). [Colin Barker, Feb 09 2012]

%t c[n_] := 3 n - 2;

%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}] (* A192311 *)

%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192312 *)

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

%Y Cf. A192232, A192312.

%K nonn

%O 1,3

%A _Clark Kimberling_, Jun 27 2011