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A169524 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169524 #8 Dec 31 2018 13:11:11
%S A169524 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A169524 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A169524 16474671000000000000,494240130000000000000,14827203900000000000000
%N A169524 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169524 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A169524 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169524 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A169524 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169524 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169524 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169524 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 +
%F A169524 2*t + 1)/(435*t^34 - 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 - 29*t^29 -
%F A169524 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 -
%F A169524 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 -
%F A169524 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 -
%F A169524 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A169524 coxG[{34,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 31 2018 *)
%K A169524 nonn
%O A169524 0,2
%A A169524 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009