cp's OEIS Frontend

A170197 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170197 #9 Nov 22 2016 16:03:18
%S A170197 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170197 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170197 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170197 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170197 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170197 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170197 <a href="/index/Rec#order_39">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, -903).
%F A170197 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170197 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170197 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170197 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170197 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^39 -
%F A170197 42*t^38 - 42*t^37 - 42*t^36 - 42*t^35 - 42*t^34 - 42*t^33 - 42*t^32 -
%F A170197 42*t^31 - 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 -
%F A170197 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 -
%F A170197 42*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 -
%F A170197 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 A170197 42*t^2 - 42*t + 1)
%t A170197 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-42 t^Range[38]]+ 903t^39+ 1},CoefficientList[Series[num/den,{t,0,25}],t]] (* _Harvey P. Dale_, Sep 10 2011 *)
%K A170197 nonn
%O A170197 0,2
%A A170197 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009