A193045 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 1, 3, 8, 21, 49, 105, 210, 399, 729, 1293, 2242, 3821, 6427, 10703, 17690, 29073, 47579, 77621, 126340, 205291, 333171, 540233, 875428, 1417961, 2295989, 3716875, 6016140, 9736669, 15756869, 25498033, 41259862, 66763351, 108029197

Offset

0,4

Comments

The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+n(-1+n^2)/6, 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..34.

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*(1-4*x+7*x^2-4*x^3+x^4) / ( (x^2+x-1)*(x-1)^4 ). - R. J. Mathar, May 12 2014

Mathematica

(See A193044.)

Crossrefs

Cf. A192232, A192744, A192951, A193044.

Sequence in context: A071078 A179903 A363601 * A238831 A322059 A259714

Adjacent sequences: A193042 A193043 A193044 * A193046 A193047 A193048

Keyword

nonn

Author

Clark Kimberling, Jul 15 2011

Status

approved