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A163452 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163452 #16 Sep 08 2022 08:45:46
%S A163452 1,18,306,5202,88434,1503225,25552224,434343744,7383094560,
%T A163452 125499873024,2133281378232,36262103930496,616393221671808,
%U A163452 10477621608796800,178101495469706112,3027418232198243904,51460888233840150528
%N A163452 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163452 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A163452 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163452 G. C. Greubel, <a href="/A163452/b163452.txt">Table of n, a(n) for n = 0..800</a>
%H A163452 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, -136).
%F A163452 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%F A163452 a(n) = 16*a(n-1)+16*a(n-2)+16*a(n-3)+16*a(n-4)-136*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163452 CoefficientList[Series[(1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6), {x, 0, 20}], x] (* or *)  LinearRecurrence[{16,16,16,16,-136}, {1, 18, 306, 5202, 88434, 1503225}, 20] (* _G. C. Greubel_, Dec 24 2016 *)
%t A163452 coxG[{5, 136, -16}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 13 2019 *)
%o A163452 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)) \\ _G. C. Greubel_, Dec 24 2016
%o A163452 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6) )); // _G. C. Greubel_, May 13 2019
%o A163452 (Sage) ((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 13 2019
%K A163452 nonn
%O A163452 0,2
%A A163452 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009