A192340 Constant term of the reduction of n-th polynomial at A158985 by x^2->x+1.
1, 3, 19, 1091, 4270307, 65975813893475, 15748607358316275150858234851, 897339846665475127909937786392825941994036757434025817827, 2913308988276889310145046342161059349226587591969604604068795694857825566722967409631885309325418272374141705507555
Offset: 1
Keywords
Examples
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,...)
Programs
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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 *)
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