A163519 - OEIS

%I #19 Sep 08 2022 08:45:46

%S 1,24,552,12696,292008,6715908,154459536,3552423600,81702391056,

%T 1879077904176,43217018799372,993950655137880,22859927229943848,

%U 525756756894338904,12091909332851083560,278102505382114851108

%N Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A170743, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A163519/b163519.txt">Table of n, a(n) for n = 0..730</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, -253).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

%F a(n) = 22*a(n-1)+22*a(n-2)+22*a(n-3)+22*a(n-4)-253*a(n-5). - _Wesley Ivan Hurt_, May 10 2021

%t CoefficientList[Series[(1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)

%t coxG[{5,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 16 2018 *)

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)) \\ _G. C. Greubel_, Jul 27 2017

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6) )); // _G. C. Greubel_, May 16 2019

%o (Sage) ((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019

%K nonn,easy

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009