A192342 Constant term of the reduction of n-th polynomial at A158983 by x^2->x+2.

2, 7, 100, 28051, 2357659852, 16675673548656023155, 834234264904007920903714901139450715276, 2087840426219791385723375854976408025594408461778898567573217959566013061037427

Offset

1,1

Comments

For an introduction to reductions of polynomials by substitutions such as x^2->x+2, see A192232.

Links

Table of n, a(n) for n=1..8.

Example

The first three polynomials at A158983 and their reductions are as follows:
p0(x)=2+x -> 2+x
p1(x)=5+4x+x^2 -> 7+5x
p2(x)=26+40x+26x^2+8x^3+x^4 -> 100+95x.
From these, we read
A192342=(2,7,100,...) and A192343=(1,5,95,...)

Mathematica

q[x_] := x + 2;
p[0, x_] := x + 2;
p[n_, x_] := 1 + p[n - 1, x]^2 /; n > 0  (* polynomials defined at A158983 *)
Table[Expand[p[n, x]], {n, 0, 4}]
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, 9}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 9}]
  (* A192342 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 9}]
  (* A192343 *)

Crossrefs

Cf. A192232, A192343.

Sequence in context: A219280 A277434 A322642 * A102598 A206157 A102747

Adjacent sequences: A192339 A192340 A192341 * A192343 A192344 A192345

Keyword

nonn

Author

Clark Kimberling, Jun 28 2011

Status

approved