cp's OEIS Frontend

A170008 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170008 #8 Jun 22 2020 17:08:05
%S A170008 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170008 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170008 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170008 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170008 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170008 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170008 <a href="/index/Rec#order_35">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, -1035).
%F A170008 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170008 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170008 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170008 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A170008 + 2*t^2 + 2*t + 1)/(1035*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 -
%F A170008 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 -
%F A170008 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 -
%F A170008 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 -
%F A170008 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 -
%F A170008 45*t + 1)
%t A170008 coxG[{35,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 22 2020 *)
%K A170008 nonn
%O A170008 0,2
%A A170008 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009