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A163669 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163669 #19 Sep 08 2022 08:45:46
%S A163669 1,40,1560,60840,2372760,92536860,3608907120,140746192080,
%T A163669 5489055252720,214071351558480,8348712382781940,325597040159662440,
%U A163669 12698177599143380760,495224754685478312040,19313602738540732379160
%N A163669 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163669 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A163669 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163669 G. C. Greubel, <a href="/A163669/b163669.txt">Table of n, a(n) for n = 0..625</a>
%H A163669 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, -741).
%F A163669 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
%F A163669 a(n) = 38*a(n-1)+38*a(n-2)+38*a(n-3)+38*a(n-4)-741*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163669 CoefficientList[Series[(1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Aug 01 2017 *)
%t A163669 coxG[{5, 741, -38}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 23 2019 *)
%o A163669 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6)) \\ _G. C. Greubel_, Aug 01 2017
%o A163669 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6) )); // _G. C. Greubel_, May 23 2019
%o A163669 (Sage) ((1+x)*(1-x^5)/(1-39*x+779*x^5-741*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 23 2019
%o A163669 (GAP) a:=[40, 1560, 60840, 2372760, 92536860];; for n in [6..20] do a[n]:=38*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -741*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, May 23 2019
%K A163669 nonn
%O A163669 0,2
%A A163669 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009