cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A192469 Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).

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%I A192469 #7 Nov 12 2012 09:55:44
%S A192469 2,8,44,224,1178,6200,32786,173600,919988,4877072,25858754,137115440,
%T A192469 727074530,3855471416,20444603516,108412922240,574888887530,
%U A192469 3048505597160,16165538467442,85722217226576,454565670533252,2410459729834544
%N A192469 Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).
%C A192469 For an introduction to reductions of polynomials by substitutions such as x^2->x+3, see A192232.
%F A192469 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 A192469 The first four polynomials p(n,x) and their reductions are as follows:
%e A192469 p(1,x)=1+x+x^2 -> 4+2x
%e A192469 p(2,x)=1+x^2+x^4 -> 16+8x
%e A192469 p(3,x)=1+x^3+x^6 -> 61+44x
%e A192469 p(4,x)=1+x^4+x^8 -> 304+224x.
%e A192469 From these, read
%e A192469 A192468=(4,16,61,304,...) and A192469=(2,8,44,224,...)
%t A192469 (See A192468.)
%Y A192469 Cf. A192232, A192468.
%K A192469 nonn
%O A192469 1,1
%A A192469 _Clark Kimberling_, Jul 01 2011