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A170200 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170200 #8 Jan 08 2019 17:22:10
%S A170200 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170200 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170200 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170200 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170200 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170200 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170200 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A170200 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 A170200 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 A170200 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 A170200 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 A170200 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^39 -
%F A170200 45*t^38 - 45*t^37 - 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 -
%F A170200 45*t^31 - 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 -
%F A170200 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 -
%F A170200 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 -
%F A170200 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 -
%F A170200 45*t^2 - 45*t + 1)
%t A170200 coxG[{39,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 08 2019 *)
%K A170200 nonn
%O A170200 0,2
%A A170200 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009