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A163593 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163593 #18 Sep 08 2022 08:45:46
%S A163593 1,34,1122,37026,1221858,40320753,1330566336,43908078720,
%T A163593 1448946455616,47814568344576,1577858820890352,52068617261591040,
%U A163593 1718240483647446528,56701147733816154624,1871111864101388705280,61745833160498214613248
%N A163593 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163593 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A163593 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163593 G. C. Greubel, <a href="/A163593/b163593.txt">Table of n, a(n) for n = 0..655</a>
%H A163593 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, -528).
%F A163593 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%F A163593 a(n) = 32*a(n-1)+32*a(n-2)+32*a(n-3)+32*a(n-4)-528*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163593 coxG[{5,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 04 2016 *)
%t A163593 CoefficientList[Series[(1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 29 2017 *)
%o A163593 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)) \\ _G. C. Greubel_, Jul 29 2017
%o A163593 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6) )); // _G. C. Greubel_, Apr 28 2019
%o A163593 (Sage) ((1+x)*(1-x^5)/(1-33*x+560*x^5-528*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%K A163593 nonn
%O A163593 0,2
%A A163593 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009