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A170293 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170293 #8 Nov 22 2016 12:02:04
%S A170293 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170293 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170293 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170293 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170293 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170293 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170293 <a href="/index/Rec#order_41">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, -903).
%F A170293 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 A170293 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 A170293 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 A170293 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 A170293 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 A170293 1)/(903*t^41 - 42*t^40 - 42*t^39 - 42*t^38 - 42*t^37 - 42*t^36 - 42*t^35
%F A170293 - 42*t^34 - 42*t^33 - 42*t^32 - 42*t^31 - 42*t^30 - 42*t^29 - 42*t^28 -
%F A170293 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 -
%F A170293 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 -
%F A170293 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 -
%F A170293 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1)
%t A170293 coxG[{41,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 23 2015 *)
%K A170293 nonn
%O A170293 0,2
%A A170293 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009