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
Keywords
Examples
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,...)
Programs
-
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 *)
Comments