A193049 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 1, 2, 4, 12, 37, 105, 268, 625, 1355, 2772, 5414, 10188, 18605, 33161, 57954, 99683, 169265, 284452, 474066, 784852, 1292567, 2119923, 3465620, 5651323, 9197673, 14947276, 24263704, 39353486, 63787101, 103341963, 167366400, 270986619

Offset

0,4

Comments

The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+n(4-5*n^2+n^4)/120, 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..33.

Index entries for linear recurrences with constant coefficients, signature (7,-20,29,-20,1,8,-5,1).

Formula

a(n)=7*a(n-1)-20*a(n-2)+29*a(n-3)-20*a(n-4)+*a(n-5)+8*a(n-6)-5*a(n-7)+a(n-8).

G.f.: -x*(x^2-x+1)*(x^4-5*x^3+9*x^2-5*x+1) / ( (x^2+x-1)*(x-1)^6 ). - R. J. Mathar, May 12 2014

Mathematica

(See A193048.)

Crossrefs

Cf. A192232, A192744, A192951, A193048.

Sequence in context: A255432 A275539 A356062 * A114500 A148212 A139627

Adjacent sequences: A193046 A193047 A193048 * A193050 A193051 A193052

Keyword

nonn

Author

Clark Kimberling, Jul 15 2011

Status

approved