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A170392 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170392 #8 Oct 05 2017 11:05:39
%S A170392 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A170392 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A170392 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A170392 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170392 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A170392 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170392 <a href="/index/Rec#order_43">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, -1035).
%F A170392 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170392 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170392 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 A170392 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 A170392 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 A170392 + 2*t^2 + 2*t + 1)/(1035*t^43 - 45*t^42 - 45*t^41 - 45*t^40 - 45*t^39 -
%F A170392 45*t^38 - 45*t^37 - 45*t^36 - 45*t^35 - 45*t^34 - 45*t^33 - 45*t^32 -
%F A170392 45*t^31 - 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 -
%F A170392 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 -
%F A170392 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 -
%F A170392 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 -
%F A170392 45*t^2 - 45*t + 1)
%t A170392 coxG[{43,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 05 2017 *)
%K A170392 nonn
%O A170392 0,2
%A A170392 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009