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A163668 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163668 #16 Sep 08 2022 08:45:46
%S A163668 1,39,1482,56316,2140008,81319563,3090115236,117423309705,
%T A163668 4462045136796,169556171182476,6443075832883092,244834652131935645,
%U A163668 9303632060115383718,353534798919570074859,13434200024194718979990
%N A163668 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163668 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A163668 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163668 G. C. Greubel, <a href="/A163668/b163668.txt">Table of n, a(n) for n = 0..630</a>
%H A163668 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, -703).
%F A163668 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
%F A163668 a(n) = 37*a(n-1)+37*a(n-2)+37*a(n-3)+37*a(n-4)-703*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163668 CoefficientList[Series[(1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Aug 01 2017 *)
%t A163668 coxG[{5, 703, -37}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 23 2019 *)
%o A163668 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)) \\ _G. C. Greubel_, Aug 01 2017
%o A163668 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6) )); // _G. C. Greubel_, May 23 2019
%o A163668 (Sage) ((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 23 2019
%o A163668 (GAP) a:=[39, 1482, 56316, 2140008, 81319563];; for n in [6..20] do a[n]:=37*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -703*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, May 23 2019
%K A163668 nonn
%O A163668 0,2
%A A163668 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009