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%I #21 Sep 08 2022 08:45:46
%S 1,8,56,392,2744,19180,134064,937104,6550320,45786384,320044452,
%T 2237094216,15637173048,109303031880,764022547512,5340478146444,
%U 37329666414768,260932440209616,1823904280240560,12748996716570576
%N Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A003950, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A163347/b163347.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6, 6, 6, 6, -21).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
%F a(n) = 6*a(n-1)+6*a(n-2)+6*a(n-3)+6*a(n-4)-21*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{6,6,6,6,-21}, {1,8,56,392,2744,19180}, 30] (* _G. C. Greubel_, Dec 19 2016 *)
%t coxG[{5, 21, -6}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 12 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6)) \\ _G. C. Greubel_, Dec 19 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6) )); // _G. C. Greubel_, May 12 2019
%o (Sage) ((1+x)*(1-x^5)/(1-7*x+27*x^5-21*x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 12 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009