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A163514 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163514 #17 Sep 08 2022 08:45:46
%S A163514 1,22,462,9702,203742,4278351,89840520,1886549280,39615400440,
%T A163514 831878586000,17468509071090,366818925627000,7702782398341800,
%U A163514 161749714998425400,3396561002126245800,71323937982067871100
%N A163514 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163514 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A163514 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163514 G. C. Greubel, <a href="/A163514/b163514.txt">Table of n, a(n) for n = 0..750</a>
%H A163514 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, -210).
%F A163514 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%F A163514 a(n) = -210*a(n-5) + 20*Sum_{k=1..4} a(n-k). - _Wesley Ivan Hurt_, May 05 2021
%t A163514 CoefficientList[Series[(1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 27 2017 *)
%t A163514 coxG[{5, 210, -20}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 16 2019 *)
%o A163514 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6)) \\ _G. C. Greubel_, Jul 27 2017
%o A163514 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6) )); // _G. C. Greubel_, May 16 2019
%o A163514 (Sage) ((1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K A163514 nonn,easy
%O A163514 0,2
%A A163514 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009