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A170389 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170389 #8 Mar 01 2019 16:31:56
%S A170389 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170389 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170389 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170389 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170389 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170389 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170389 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A170389 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 A170389 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 A170389 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 A170389 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 A170389 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 A170389 + 2*t^2 + 2*t + 1)/(903*t^43 - 42*t^42 - 42*t^41 - 42*t^40 - 42*t^39 -
%F A170389 42*t^38 - 42*t^37 - 42*t^36 - 42*t^35 - 42*t^34 - 42*t^33 - 42*t^32 -
%F A170389 42*t^31 - 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 -
%F A170389 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 -
%F A170389 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 -
%F A170389 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 -
%F A170389 42*t^2 - 42*t + 1)
%t A170389 coxG[{43,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 01 2019 *)
%K A170389 nonn
%O A170389 0,2
%A A170389 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009