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A170488 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170488 #8 Jun 28 2020 16:18:00
%S A170488 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170488 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170488 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170488 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170488 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170488 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170488 <a href="/index/Rec#order_45">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, -1035).
%F A170488 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170488 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170488 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170488 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170488 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170488 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^45 - 45*t^44 - 45*t^43
%F A170488 - 45*t^42 - 45*t^41 - 45*t^40 - 45*t^39 - 45*t^38 - 45*t^37 - 45*t^36 -
%F A170488 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 - 45*t^30 - 45*t^29 -
%F A170488 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 -
%F A170488 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 -
%F A170488 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 -
%F A170488 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1)
%t A170488 coxG[{45,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 28 2020 *)
%K A170488 nonn
%O A170488 0,2
%A A170488 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009