OFFSET
0,2
COMMENTS
MATHEMATICA
q = x^2; s = x + 1; z = 40;
p[0, n_] := 1;
p[n_, x_] := x*p[n - 1, x] + Floor[(n + 1)*GoldenRatio] /; n > 0;
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}]
(* A192457 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A023611 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved