A192469 - OEIS

A192469

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

%I #7 Nov 12 2012 09:55:44

%S 2,8,44,224,1178,6200,32786,173600,919988,4877072,25858754,137115440,

%T 727074530,3855471416,20444603516,108412922240,574888887530,

%U 3048505597160,16165538467442,85722217226576,454565670533252,2410459729834544

%N Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).

%C For an introduction to reductions of polynomials by substitutions such as x^2->x+3, see A192232.

%F Empirical G.f.: -2*x*(x-1)*(3*x-1)/((3*x^2+x-1)*(9*x^2-7*x+1)). [_Colin Barker_, Nov 12 2012]

%e The first four polynomials p(n,x) and their reductions are as follows:

%e p(1,x)=1+x+x^2 -> 4+2x

%e p(2,x)=1+x^2+x^4 -> 16+8x

%e p(3,x)=1+x^3+x^6 -> 61+44x

%e p(4,x)=1+x^4+x^8 -> 304+224x.

%e From these, read

%e A192468=(4,16,61,304,...) and A192469=(2,8,44,224,...)

%t (See A192468.)

%Y Cf. A192232, A192468.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jul 01 2011