cp's OEIS Frontend

A170190 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170190 #9 Nov 22 2016 15:59:37
%S A170190 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A170190 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A170190 4870003042163884032,175320109517899825152,6311523942644393705472
%N A170190 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170190 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A170190 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170190 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
%F A170190 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170190 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 A170190 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 A170190 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 A170190 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^39 -
%F A170190 35*t^38 - 35*t^37 - 35*t^36 - 35*t^35 - 35*t^34 - 35*t^33 - 35*t^32 -
%F A170190 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 -
%F A170190 35*t^24 - 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 -
%F A170190 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 -
%F A170190 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 -
%F A170190 35*t^2 - 35*t + 1)
%t A170190 With[{num=Total[2t^Range[38]]+t^39+1, den=Total[-35 t^Range[38]]+ 630t^39+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 24 2011 *)
%K A170190 nonn
%O A170190 0,2
%A A170190 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009