cp's OEIS Frontend

A169184 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169184 #8 Nov 25 2016 14:00:14
%S A169184 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A169184 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A169184 2576581829865418752,66991127576500887552,1741769316989023076352
%N A169184 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169184 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A169184 First disagreement at index 27: a(27) = 166215228665593247391510205786805501601, A170746(27) = 166215228665593247391510205786805501952. - Klaus Brockhaus, May 07 2011
%C A169184 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169184 <a href="/index/Rec#order_27">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, 25, 25, 25, 25, 25, 25, 25, -325).
%F A169184 G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*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^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*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).
%Y A169184 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A169184 nonn
%O A169184 0,2
%A A169184 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009