cp's OEIS Frontend

A168848 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168848 #10 Aug 28 2022 15:05:11
%S A168848 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A168848 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A168848 2576581829865418752,66991127576500887552,1741769316989023076352
%N A168848 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168848 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A168848 First disagreement at index 20: a(20) = 20694616160409771042814820001, A170746(20) = 20694616160409771042814820352. - Klaus Brockhaus, Apr 02 2011
%C A168848 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168848 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A168848 G.f.: (t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
%t A168848 coxG[{20,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 28 2022 *)
%Y A168848 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A168848 nonn
%O A168848 0,2
%A A168848 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009