A192759 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.

0, 1, 2, 4, 7, 12, 21, 35, 58, 95, 155, 253, 411, 667, 1081, 1751, 2836, 4591, 7431, 12026, 19461, 31492, 50958, 82455, 133418, 215878, 349302, 565186, 914494, 1479686, 2394186, 3873879, 6268072, 10141958, 16410037, 26552002, 42962047

Offset

0,3

Comments

The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+floor((n+5)/5) for n>0, where p(0,x)=1. For discussions of polynomial reduction, see A192232 and A192744.

Links

Table of n, a(n) for n=0..36.

Formula

Conjecture: G.f.: -x / ( (x^2+x-1)*(x^4+x^3+x^2+x+1)*(x-1)^2 ), partial sums of A124502. - R. J. Mathar, May 04 2014

Mathematica

p[0, n_] := 1; p[n_, x_] := x*p[n - 1, x] + Floor[(n + 5)/5] /; 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}]
(* A124502 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A192759 *)

Crossrefs

Cf. A192744, A192232.

Sequence in context: A100482 A301762 A003293 * A289249 A094974 A306306

Adjacent sequences: A192756 A192757 A192758 * A192760 A192761 A192762

Keyword

nonn

Author

Clark Kimberling, Jul 09 2011

Status

approved