cp's OEIS Frontend

A170584 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170584 #6 Nov 21 2016 13:10:36
%S A170584 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170584 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170584 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170584 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170584 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170584 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170584 <a href="/index/Rec#order_47">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, -1035).
%F A170584 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170584 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170584 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 A170584 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 A170584 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 A170584 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^47 -
%F A170584 45*t^46 - 45*t^45 - 45*t^44 - 45*t^43 - 45*t^42 - 45*t^41 - 45*t^40 -
%F A170584 45*t^39 - 45*t^38 - 45*t^37 - 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 -
%F A170584 45*t^32 - 45*t^31 - 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 -
%F A170584 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 -
%F A170584 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 -
%F A170584 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4
%F A170584 - 45*t^3 - 45*t^2 - 45*t + 1)
%K A170584 nonn
%O A170584 0,2
%A A170584 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009