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A163527 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163527 #21 Sep 08 2022 08:45:46
%S A163527 1,27,702,18252,474552,12338001,320778900,8340014475,216834216300,
%T A163527 5637529462500,146571601954050,3810753388040625,99076773337132500,
%U A163527 2575922925294444375,66972093393463976250,1741224960366454777500
%N A163527 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163527 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A163527 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163527 G. C. Greubel, <a href="/A163527/b163527.txt">Table of n, a(n) for n = 0..700</a>
%H A163527 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, -325).
%F A163527 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
%F A163527 a(n) = 25*a(n-1)+25*a(n-2)+25*a(n-3)+25*a(n-4)-325*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163527 CoefficientList[Series[(1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t A163527 coxG[{5, 325, -25}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o A163527 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o A163527 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6) )); // _G. C. Greubel_, May 16 2019
%o A163527 (Sage) ((1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K A163527 nonn
%O A163527 0,2
%A A163527 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009