A193047 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 2, 19, 102, 377, 1104, 2777, 6282, 13155, 25998, 49153, 89792, 159681, 278034, 476131, 804790, 1346457, 2234768, 3686201, 6051290, 9897491, 16143262, 26275009, 42698112, 69304897, 112393634, 182155507, 295080582, 477850745

Offset

0,3

Comments

The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+n^4, 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..29.

Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1).

Formula

a(n)=6*a(n-1)-14*a(n-2)+15*a(n-3)-5*a(n-4)-4*a(n-5)+4*a(n-6)-a(n-7).

G.f.: -x*(-1+4*x-21*x^2-x^3-6*x^4+x^5) / ( (x^2+x-1)*(x-1)^5 ). - R. J. Mathar, May 12 2014

Mathematica

(See A193046.)

Crossrefs

Cf. A192232, A192744, A192951, A193046.

Sequence in context: A041393 A107123 A360816 * A055875 A089659 A396762

Adjacent sequences: A193044 A193045 A193046 * A193048 A193049 A193050

Keyword

nonn

Author

Clark Kimberling, Jul 15 2011

Status

approved