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A170142 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170142 #15 May 14 2017 17:40:28
%S A170142 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A170142 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A170142 4870003042163884032,175320109517899825152,6311523942644393705472
%N A170142 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170142 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A170142 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170142 Matthew House, <a href="/A170142/b170142.txt">Table of n, a(n) for n = 0..639</a>
%H A170142 <a href="/index/Rec#order_38">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, -630).
%F A170142 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 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 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 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^38 - 35*t^37 - 35*t^36 - 35*t^35 - 35*t^34 - 35*t^33 - 35*t^32 - 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
%t A170142 coxG[{38,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 21 2014 *)
%K A170142 nonn
%O A170142 0,2
%A A170142 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009