A193007 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 1, 9, 36, 108, 268, 591, 1201, 2303, 4232, 7534, 13096, 22357, 37649, 62749, 103772, 170616, 279300, 455747, 741905, 1205651, 1956816, 3173114, 5142096, 8329033, 13486753, 21833361, 35339796, 57195108, 92559292, 149781399, 242370481

Offset

0,4

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..32.

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*(2*x^4-6*x^3+13*x^2-4*x+1)/((x-1)^4*(x^2+x-1)). [Colin Barker, Nov 12 2012]

Mathematica

(See A193006.)
LinearRecurrence[{5, -9, 6, 1, -3, 1}, {0, 1, 1, 9, 36, 108}, 40] (* Harvey P. Dale, Sep 13 2021 *)

Crossrefs

Cf. A192232, A192744, A192951, A193006.

Sequence in context: A103158 A298442 A212104 * A369888 A259279 A168569

Adjacent sequences: A193004 A193005 A193006 * A193008 A193009 A193010

Keyword

nonn,easy

Author

Clark Kimberling, Jul 14 2011

Status

approved