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A192256 0-sequence of reduction of (n^3) by x^2 -> x+1.

%I A192256 #14 Aug 23 2025 08:03:25
%S A192256 1,1,28,92,342,990,2705,6801,16278,37278,82532,177572,373105,768241,
%T A192256 1554616,3098808,6095738,11851922,22805745,43477745,82197986,
%U A192256 154231706,287411688,532248552,980014177,1794978145,3271695220,5936514356,10726952958
%N A192256 0-sequence of reduction of (n^3) by x^2 -> x+1.
%C A192256 See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%F A192256 Empirical g.f.: x*(1-4*x+29*x^2-36*x^3+43*x^4-16*x^5+2*x^6)/(1-x)/(1-x-x^2)^4. - _Colin Barker_, Feb 10 2012
%t A192256 c[n_] := n^3;  (* A000578 *)
%t A192256 Table[c[n], {n, 1, 15}]
%t A192256 q[x_] := x + 1;
%t A192256 p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
%t A192256 reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
%t A192256    x^y_?OddQ -> x q[x]^((y - 1)/2)};
%t A192256 t = Table[
%t A192256   Last[Most[
%t A192256     FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
%t A192256    30}]
%t A192256 Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192256 *)
%t A192256 Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192257 *)
%t A192256 (* _Peter J. C. Moses_, Jun 20 2011 *)
%Y A192256 Cf. A192232, A192257.
%K A192256 nonn,changed
%O A192256 1,3
%A A192256 _Clark Kimberling_, Jun 27 2011