OFFSET
0,3
COMMENTS
For an introduction to reductions of polynomials by substitutions such as x^2 -> x+1, see A192232.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..97
EXAMPLE
MATHEMATICA
q = x^2; s = x + 1; z = 26;
p[0, x]:= 1;
p[n_, x_]:= (x + Fibonacci[n+1])*p[n-1, x];
Table[Expand[p[n, x]], {n, 0, 7}]
reduce[{p1_, q_, s_, x_}]:= FixedPoint[(s PolynomialQuotient @@ #1 + PolynomialRemainder @@ #1 &)[{#1, q, x}] &, p1]
t = Table[reduce[{p[n, x], q, s, x}], {n, 0, z}];
u1 = Table[Coefficient[Part[t, n], x, 0], {n, 1, z}] (* A192943 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}] (* A192944 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 13 2011
STATUS
approved