cp's OEIS Frontend

A170344 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170344 #8 May 10 2019 17:01:53
%S A170344 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170344 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170344 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170344 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170344 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170344 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170344 <a href="/index/Rec#order_42">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, -1035).
%F A170344 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170344 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170344 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170344 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170344 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A170344 2*t + 1)/(1035*t^42 - 45*t^41 - 45*t^40 - 45*t^39 - 45*t^38 - 45*t^37 -
%F A170344 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 - 45*t^30 -
%F A170344 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 -
%F A170344 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 -
%F A170344 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 -
%F A170344 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 A170344 coxG[{42,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 10 2019 *)
%K A170344 nonn
%O A170344 0,2
%A A170344 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009