cp's OEIS Frontend

A170585 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170585 #9 Nov 21 2016 13:11:09
%S A170585 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A170585 24317909782224,1142941759764528,53718262708932816,
%U A170585 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A170585 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170585 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A170585 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170585 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).
%F A170585 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 A170585 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 A170585 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 A170585 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 A170585 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 A170585 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^47 -
%F A170585 46*t^46 - 46*t^45 - 46*t^44 - 46*t^43 - 46*t^42 - 46*t^41 - 46*t^40 -
%F A170585 46*t^39 - 46*t^38 - 46*t^37 - 46*t^36 - 46*t^35 - 46*t^34 - 46*t^33 -
%F A170585 46*t^32 - 46*t^31 - 46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 -
%F A170585 46*t^25 - 46*t^24 - 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 -
%F A170585 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 -
%F A170585 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4
%F A170585 - 46*t^3 - 46*t^2 - 46*t + 1)
%t A170585 With[{num=Total[2t^Range[46]]+t^47+1,den=Total[-46 t^Range[46]]+ 1081t^47+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 12 2011 *)
%K A170585 nonn
%O A170585 0,2
%A A170585 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009