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A192755 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)