cp's OEIS Frontend

A164091 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A164091 #12 Sep 08 2022 08:45:47
%S A164091 1,41,1640,65600,2624000,104960000,4198399180,167935934400,
%T A164091 6717436064820,268697390145600,10747893507936000,429915656401920000,
%U A164091 17196622899456671580,687864781713487950000,27514585897949409744420
%N A164091 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164091 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A164091 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164091 G. C. Greubel, <a href="/A164091/b164091.txt">Table of n, a(n) for n = 0..620</a>
%H A164091 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, -780).
%F A164091 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
%F A164091 G.f.: (1+x)*(1-x^6)/(1 -40*x +819*x^6 -780*x^7). - _G. C. Greubel_, Apr 25 2019
%t A164091 coxG[{6,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 25 2015 *)
%t A164091 CoefficientList[Series[(1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7), {x,0,20}], x] (* _G. C. Greubel_, Apr 25 2019 *)
%o A164091 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7)) \\ _G. C. Greubel_, Apr 25 2019
%o A164091 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7) )); // _G. C. Greubel_, Apr 25 2019
%o A164091 (Sage) ((1+x)*(1-x^6)/(1-40*x+819*x^6-780*x^7)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A164091 nonn
%O A164091 0,2
%A A164091 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009