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A163567 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163567 #21 Sep 08 2022 08:45:46
%S A163567 1,33,1056,33792,1081344,34602480,1107262464,35431858704,
%T A163567 1133802193920,36281117097984,1160978047975152,37150731170716416,
%U A163567 1188805274075570448,38041188830863975680,1217299484804824768512,38952989673757190287344
%N A163567 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163567 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A163567 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163567 G. C. Greubel, <a href="/A163567/b163567.txt">Table of n, a(n) for n = 0..660</a>
%H A163567 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, -496).
%F A163567 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(496*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%F A163567 a(n) = 31*a(n-1)+31*a(n-2)+31*a(n-3)+31*a(n-4)-496*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163567 coxG[{5,496,-31}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 08 2015 *)
%t A163567 CoefficientList[Series[(1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 28 2017 *)
%o A163567 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6)) \\ _G. C. Greubel_, Jul 28 2017
%o A163567 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6) )); // _G. C. Greubel_, May 18 2019
%o A163567 (Sage) ((1+x)*(1-x^5)/(1-32*x+527*x^5-496*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 18 2019
%K A163567 nonn,easy
%O A163567 0,2
%A A163567 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009