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A170680 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170680 #8 May 05 2019 14:01:03
%S A170680 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170680 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170680 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170680 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170680 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170680 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170680 <a href="/index/Rec#order_49">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, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A170680 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170680 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170680 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170680 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170680 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170680 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 +
%F A170680 1)/(1035*t^49 - 45*t^48 - 45*t^47 - 45*t^46 - 45*t^45 - 45*t^44 -
%F A170680 45*t^43 - 45*t^42 - 45*t^41 - 45*t^40 - 45*t^39 - 45*t^38 - 45*t^37 -
%F A170680 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 - 45*t^30 -
%F A170680 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 -
%F A170680 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 -
%F A170680 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 -
%F A170680 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1)
%t A170680 coxG[{49,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 05 2019 *)
%K A170680 nonn
%O A170680 0,2
%A A170680 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009