A192353 -id:A192353 - cp's OEIS frontend

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

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Clark Kimberling, Jun 29 2011

nonn

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

Cf. A192232, A192353.

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(See A192353.)
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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]

cp's OEIS Frontend

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.

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