cp's OEIS Frontend

A168946 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

%I A168946 #10 Nov 25 2016 09:55:10
%S A168946 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A168946 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A168946 6734329687587160064,188561231252440481792,5279714475068333490176
%N A168946 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
%C A168946 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A168946 First disagreement at index 22: a(22) = 71238809975868630097920222297706, A170748(22) = 71238809975868630097920222298112. - Klaus Brockhaus, Apr 10 2011
%C A168946 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168946 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A168946 G.f.: (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)/(378*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
%t A168946 With[{num=Total[2t^Range[21]]+t^22+1,den=Total[-27 t^Range[21]]+378t^22+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 08 2013 *)
%Y A168946 Cf. A170748 (G.f.: (1+x)/(1-28*x)).
%K A168946 nonn
%O A168946 0,2
%A A168946 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009