cp's OEIS Frontend

A170296 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170296 #8 Nov 22 2016 12:03:45
%S A170296 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170296 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170296 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170296 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170296 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170296 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170296 <a href="/index/Rec#order_41">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, -1035).
%F A170296 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170296 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 A170296 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 A170296 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 A170296 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 A170296 1)/(1035*t^41 - 45*t^40 - 45*t^39 - 45*t^38 - 45*t^37 - 45*t^36 -
%F A170296 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 - 45*t^31 - 45*t^30 - 45*t^29 -
%F A170296 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 -
%F A170296 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 -
%F A170296 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 -
%F A170296 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1)
%t A170296 coxG[{41,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 19 2015 *)
%K A170296 nonn
%O A170296 0,2
%A A170296 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009