cp's OEIS Frontend

A170057 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170057 #9 Nov 26 2016 09:50:13
%S A170057 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A170057 24317909782224,1142941759764528,53718262708932816,
%U A170057 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A170057 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170057 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A170057 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170057 <a href="/index/Rec#order_36">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, -1081).
%F A170057 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170057 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170057 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170057 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
%F A170057 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^36 - 46*t^35 - 46*t^34 - 46*t^33 -
%F A170057 46*t^32 - 46*t^31 - 46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 -
%F A170057 46*t^25 - 46*t^24 - 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 -
%F A170057 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 -
%F A170057 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 A170057 - 46*t^3 - 46*t^2 - 46*t + 1)
%t A170057 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-46 t^Range[35]]+ 1081t^36+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Sep 22 2011 *)
%K A170057 nonn
%O A170057 0,2
%A A170057 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009