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.

A193041 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

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%I A193041 #14 Feb 18 2025 08:17:50
%S A193041 0,1,3,13,44,122,292,631,1267,2411,4408,7820,13560,23109,38867,64721,
%T A193041 106964,175782,287660,469275,763795,1241071,2014128,3265848,5292144,
%U A193041 8571817,13879587,22468981,36368252,58859186,95251828,154138015
%N A193041 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
%C A193041 The titular polynomials are defined recursively:  p(n,x)=x*p(n-1,x)+1+n^3, with p(0,x)=1.  For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.
%H A193041 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,6,1,-3,1).
%F A193041 a(n) = 5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).
%F A193041 G.f.: -x*(7*x^2-2*x+1)/((x-1)^4*(x^2+x-1)). [_Colin Barker_, Nov 12 2012]
%t A193041 (See A193008.)
%Y A193041 Cf. A192232, A192744, A192951, A193008.
%K A193041 nonn,easy
%O A193041 0,3
%A A193041 _Clark Kimberling_, Jul 15 2011