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.

A163525 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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%I A163525 #19 Sep 08 2022 08:45:46
%S A163525 1,25,600,14400,345600,8294100,199051200,4777056300,114645211200,
%T A163525 2751385708800,66030872460900,1584683711924400,38031035684483100,
%U A163525 912711895976984400,21904294481198985600,525684083700365474100
%N A163525 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163525 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A163525 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163525 G. C. Greubel, <a href="/A163525/b163525.txt">Table of n, a(n) for n = 0..720</a>
%H A163525 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, -276).
%F A163525 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
%F A163525 a(n) = 23*a(n-1)+23*a(n-2)+23*a(n-3)+23*a(n-4)-276*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163525 CoefficientList[Series[(1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t A163525 coxG[{5, 276, -23}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o A163525 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o A163525 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6) )); // _G. C. Greubel_, May 16 2019
%o A163525 (Sage) ((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K A163525 nonn,easy
%O A163525 0,2
%A A163525 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009