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A163518 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163518 #17 Sep 08 2022 08:45:46
%S A163518 1,23,506,11132,244904,5387635,118522404,2607370689,57359466780,
%T A163518 1261849124844,27759379635372,610677728876061,13434280356535038,
%U A163518 295540315560771435,6501582206394337062,143028104664155140584
%N A163518 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163518 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A163518 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163518 G. C. Greubel, <a href="/A163518/b163518.txt">Table of n, a(n) for n = 0..740</a>
%H A163518 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, -231).
%F A163518 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
%F A163518 a(n) = 21*a(n-1)+21*a(n-2)+21*a(n-3)+21*a(n-4)-231*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163518 CoefficientList[Series[(1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t A163518 coxG[{5, 231, -21}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o A163518 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o A163518 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6) )); // _G. C. Greubel_, May 16 2019
%o A163518 (Sage) ((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K A163518 nonn,easy
%O A163518 0,2
%A A163518 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009