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A192340 Constant term of the reduction of n-th polynomial at A158985 by x^2->x+1. 2
1, 3, 19, 1091, 4270307, 65975813893475, 15748607358316275150858234851, 897339846665475127909937786392825941994036757434025817827, 2913308988276889310145046342161059349226587591969604604068795694857825566722967409631885309325418272374141705507555 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

The first three polynomials at A158985 and their reductions are as follows:

p0(x)=1+x -> 1+x

p1(x)=2+2x+x^2 -> 3+3x

p2(x)=5+8x+8x^2+4x^3+x^4 -> 19+27x.

From these, we read

A192340=(1,3,19,...) and A192341=(1,3,27,...)

MATHEMATICA

q[x_] := x + 1;

p[0, x_] := x + 1;

p[n_, x_] := 1 + p[n - 1, x]^2 /; n > 0  (* polynomials defined at A158985 *)

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}]

(* A192340 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 9}]

(* A192341 *)

CROSSREFS

Cf. A192232, A192341.

Sequence in context: A014015 A114301 A258669 * A248704 A098796 A120563

Adjacent sequences:  A192337 A192338 A192339 * A192341 A192342 A192343

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 28 2011

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)