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

1, 1, 28, 92, 342, 990, 2705, 6801, 16278, 37278, 82532, 177572, 373105, 768241, 1554616, 3098808, 6095738, 11851922, 22805745, 43477745, 82197986, 154231706, 287411688, 532248552, 980014177, 1794978145, 3271695220, 5936514356, 10726952958

Offset: 1

Author

Clark Kimberling, Jun 27 2011

Keywords

• nonn
• changed

Comments

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

Crossrefs

Cf. A192232, A192257.

Programs

Mathematica

c[n_] := n^3;  (* A000578 *)
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}]  (* A192256 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192257 *)
(* Peter J. C. Moses, Jun 20 2011 *)

Formula

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