A193041 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 3, 13, 44, 122, 292, 631, 1267, 2411, 4408, 7820, 13560, 23109, 38867, 64721, 106964, 175782, 287660, 469275, 763795, 1241071, 2014128, 3265848, 5292144, 8571817, 13879587, 22468981, 36368252, 58859186, 95251828, 154138015

Offset

0,3

Comments

The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+1+n^3, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (5,-9,6,1,-3,1).

Formula

a(n)=5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).

G.f.: -x*(7*x^2-2*x+1)/((x-1)^4*(x^2+x-1)). [Colin Barker, Nov 12 2012]

Mathematica

(See A193008.)

Crossrefs

Cf. A192232, A192744, A192951, A193008.

Sequence in context: A208060 A284194 A209296 * A058407 A095863 A136520

Adjacent sequences: A193038 A193039 A193040 * A193042 A193043 A193044

Keyword

nonn,easy

Author

Clark Kimberling, Jul 15 2011

Status

approved