A192358 Coefficients of x in the reduction of the polynomial p(n,x)=(1/2)((x+3)^n+(x-3)^n) by x^2->x+1.

0, 1, 1, 29, 57, 590, 1628, 11731, 39459, 236797, 899155, 4863068, 19903896, 101199149, 433857437, 2124952045, 9374498133, 44879983186, 201514230964, 951385817327, 4318344961935, 20214336758573, 92366228744351, 430111736709904

Offset

1,4

Comments

For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.

Links

Table of n, a(n) for n=1..24.

Formula

Conjecture: a(n) = 2*a(n-1)+19*a(n-2)-20*a(n-3)-55*a(n-4). G.f.: x^2*(8*x^2-x+1)/((5*x^2+5*x+1)*(11*x^2-7*x+1)). [Colin Barker, Nov 22 2012]

Mathematica

(See A192357.)

Crossrefs

Cf. A192232, A192357.

Sequence in context: A049743 A339865 A033915 * A123848 A340669 A040812

Adjacent sequences: A192355 A192356 A192357 * A192359 A192360 A192361

Keyword

nonn

Author

Clark Kimberling, Jun 29 2011

Status

approved