%I #15 Sep 08 2022 08:45:47
%S 1,48,2256,106032,4983504,234223560,11008454304,517394861664,
%T 24317441438880,1142914245838944,53716710971646072,
%U 2524673262335033136,118659072125876564688,5576949543463542381360,262115366765585626863312
%N Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A170767, 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="/A163829/b163829.txt">Table of n, a(n) for n = 0..595</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, -1081).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%F G.f.: (1+x)*(1-x^5)/(1 -47*x +1127*x^5 -1081*x^6). - _G. C. Greubel_, Apr 25 2019
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Aug 05 2017, modified Apr 25 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6)) \\ _G. C. Greubel_, Aug 05 2017, modified Apr 25 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6) )); // _G. C. Greubel_, Apr 25 2019
%o (Sage) ((1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009