OFFSET
1,2
COMMENTS
For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.
EXAMPLE
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 28 2011
STATUS
approved