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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. 1

%I #7 Nov 22 2012 08:13:48

%S 0,1,1,29,57,590,1628,11731,39459,236797,899155,4863068,19903896,

%T 101199149,433857437,2124952045,9374498133,44879983186,201514230964,

%U 951385817327,4318344961935,20214336758573,92366228744351,430111736709904

%N 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.

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

%F 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]

%t (See A192357.)

%Y Cf. A192232, A192357.

%K nonn

%O 1,4

%A _Clark Kimberling_, Jun 29 2011

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