# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a163526
Showing 1-1 of 1

%I A163526 #18 Sep 08 2022 08:45:46
%S A163526 1,26,650,16250,406250,10155925,253890000,6347047200,158671110000,
%T A163526 3966651000000,99163106355300,2478998445300000,61972980856207200,
%U A163526 1549275016079700000,38730637808401500000,968235006358878382800
%N A163526 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163526 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A163526 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163526 G. C. Greubel, <a href="/A163526/b163526.txt">Table of n, a(n) for n = 0..710</a>
%H A163526 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, 24, -300).
%F A163526 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
%F A163526 a(n) = 24*a(n-1)+24*a(n-2)+24*a(n-3)+24*a(n-4)-300*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163526 CoefficientList[Series[(1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t A163526 coxG[{5, 300, -24}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o A163526 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o A163526 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6) )); // _G. C. Greubel_, May 16 2019
%o A163526 (Sage) ((1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K A163526 nonn
%O A163526 0,2
%A A163526 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE