cp's OEIS Frontend

A170153 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170153 #12 May 14 2017 17:43:40
%S A170153 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A170153 24317909782224,1142941759764528,53718262708932816,
%U A170153 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A170153 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170153 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A170153 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170153 <a href="/index/Rec#order_38">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, -1081).
%F A170153 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170153 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170153 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170153 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170153 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^38 - 46*t^37 -
%F A170153 46*t^36 - 46*t^35 - 46*t^34 - 46*t^33 - 46*t^32 - 46*t^31 - 46*t^30 -
%F A170153 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 - 46*t^23 -
%F A170153 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 -
%F A170153 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 -
%F A170153 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%t A170153 With[{num=Total[2t^Range[37]]+t^38+1,den=Total[-46 t^Range[37]]+ 1081t^38+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 06 2011 *)
%K A170153 nonn
%O A170153 0,2
%A A170153 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009