A192755 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.

0, 1, 7, 19, 42, 82, 150, 263, 449, 753, 1248, 2052, 3356, 5469, 8891, 14431, 23398, 37910, 61394, 99395, 160885, 260381, 421372, 681864, 1103352, 1785337, 2888815, 4674283, 7563234, 12237658, 19801038, 32038847, 51840041, 83879049

Offset

0,3

Comments

The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+5n+1 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..33.

Formula

From R. J. Mathar, May 04 2014: (Start)

Conjecture: G.f.: -x*(1+4*x) / ( (x^2+x-1)*(x-1)^2 ).

a(n) = A001924(n)+4*A001924(n-1).

Partial sums of A192754. (End)

Mathematica

p[0, n_] := 1; p[n_, x_] := x*p[n - 1, x] + 5 n + 1;
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}]
  (* A192754 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
  (* A192755 *)

Crossrefs

Cf. A192754, A192744, A192232.

Sequence in context: A100620 A002177 A225279 * A141193 A104163 A145993

Adjacent sequences: A192752 A192753 A192754 * A192756 A192757 A192758

Keyword

nonn

Author

Clark Kimberling, Jul 09 2011

Status

approved