A192354 Coefficients of x in the reduction of the polynomial p(n,x)=(1/2)((x+2)^n+(x-2)^n) by x^2->x+1.

0, 1, 1, 14, 27, 165, 428, 2001, 6069, 25042, 82555, 319793, 1101816, 4131009, 14567657, 53697270, 191684283, 700312381, 2515972324, 9149426897, 32981059485, 119645675898, 432046756571, 1565346866889, 5657752486512, 20484930829825

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..26.

Formula

Empirical G.f.: x^2*(3*x^2-x+1)/((x^2+3*x+1)*(5*x^2-5*x+1)). [Colin Barker, Sep 12 2012]

Mathematica

(See A192353.)

Crossrefs

Cf. A192232, A192353.

Sequence in context: A168596 A275251 A331099 * A215970 A372446 A040182

Adjacent sequences: A192351 A192352 A192353 * A192355 A192356 A192357

Keyword

nonn

Author

Clark Kimberling, Jun 29 2011

Status

approved