cp's OEIS Frontend

A170560 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170560 #8 Nov 21 2016 12:55:25
%S A170560 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170560 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170560 295665060514131968,6504631331310903296,143101889288839872512
%N A170560 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170560 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170560 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170560 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A170560 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170560 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170560 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170560 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170560 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170560 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^47 -
%F A170560 21*t^46 - 21*t^45 - 21*t^44 - 21*t^43 - 21*t^42 - 21*t^41 - 21*t^40 -
%F A170560 21*t^39 - 21*t^38 - 21*t^37 - 21*t^36 - 21*t^35 - 21*t^34 - 21*t^33 -
%F A170560 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 - 21*t^26 -
%F A170560 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 -
%F A170560 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 -
%F A170560 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4
%F A170560 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170560 With[{num=Total[2t^Range[46]]+t^47+1,den=Total[-21 t^Range[46]]+ 231t^47+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 26 2012 *)
%K A170560 nonn
%O A170560 0,2
%A A170560 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009