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%I A192145 #8 Dec 04 2016 19:46:25
%S A192145 1,1,13,35,105,258,608,1344,2865,5910,11894,23444,45427,86755,163645,
%T A192145 305397,564647,1035446,1885050,3409610,6131441,10968416,19528188,
%U A192145 34617960,61125685,107540053,188567053,329625719,574558965,998836650
%N A192145 0-sequence of reduction of pentagonal numbers sequence by x^2 -> x+1.
%C A192145 See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%F A192145 Empirical G.f.: x*(1-3*x+12*x^2-9*x^3+4*x^4)/(1-x)/(1-x-x^2)^3. [Colin Barker, Feb 11 2012]
%t A192145 Remove["Global`*"];
%t A192145 c[n_] := n (3 n - 1)/2; (* pentagonal numbers, A000326 *)
%t A192145 Table[c[n], {n, 1, 15}]
%t A192145 q[x_] := x + 1;
%t A192145 p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
%t A192145 reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
%t A192145    x^y_?OddQ -> x q[x]^((y - 1)/2)};
%t A192145 t = Table[
%t A192145   Last[Most[
%t A192145     FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
%t A192145    30}]
%t A192145 Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192145 *)
%t A192145 Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192146 *)
%t A192145 (* by _Peter J. C. Moses_, Jun 20 2011 *)
%Y A192145 Cf. A192232, A192146.
%K A192145 nonn
%O A192145 1,3
%A A192145 _Clark Kimberling_, Jun 27 2011

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