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A164332 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A164332 #16 Sep 08 2022 08:45:47
%S A164332 1,47,2162,99452,4574792,210440432,9680258791,445291854660,
%T A164332 20483423028045,942237354119580,43342913451658140,1993773796235517600,
%U A164332 91713584389960162440,4218824411042032288125,194065901246713684538250
%N A164332 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164332 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A164332 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164332 G. C. Greubel, <a href="/A164332/b164332.txt">Table of n, a(n) for n = 0..600</a>
%H A164332 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, -1035).
%F A164332 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%F A164332 G.f.: (1+x)*(1-x^6)/(1 -46*x +1080*x^6 -1035*x^7). - _G. C. Greubel_, Apr 25 2019
%F A164332 a(n) = -1035*a(n-6) + 45*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 06 2021
%t A164332 CoefficientList[Series[(1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7), {x, 0, 20}], x] (* _G. C. Greubel_, Sep 14 2017, modified Apr 25 2019 *)
%t A164332 coxG[{6, 1035, -45}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 25 2019 *)
%o A164332 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)) \\ _G. C. Greubel_, Sep 14 2017, modified Apr 25 2019
%o A164332 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7) )); // _G. C. Greubel_, Apr 25 2019
%o A164332 (Sage) ((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A164332 nonn
%O A164332 0,2
%A A164332 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009