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A163564 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163564 #19 Sep 08 2022 08:45:46
%S A163564 1,31,930,27900,837000,25109535,753272100,22597744965,677919807900,
%T A163564 20337218005500,610105253435760,18302819007466125,549074412543683490,
%U A163564 16471927651538698875,494148687972122850750,14824186397015923722360
%N A163564 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163564 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A163564 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163564 G. C. Greubel, <a href="/A163564/b163564.txt">Table of n, a(n) for n = 0..670</a>
%H A163564 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, -435).
%F A163564 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
%F A163564 a(n) = 29*a(n-1)+29*a(n-2)+29*a(n-3)+29*a(n-4)-435*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163564 With[{num=Total[2t^Range[4]]+t^5+1, den=Total[-29 t^Range[4]]+435t^5+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Sep 16 2011 *)
%t A163564 CoefficientList[Series[(1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6), {x,0,20}], x] (* or *) coxG[{5, 435, -29}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 18 2019 *)
%o A163564 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6)) \\ _G. C. Greubel_, Jul 28 2017
%o A163564 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6) )); // _G. C. Greubel_, May 18 2019
%o A163564 (Sage) ((1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 18 2019
%K A163564 nonn
%O A163564 0,2
%A A163564 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009