cp's OEIS Frontend

A170195 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170195 #8 Nov 22 2016 16:02:13
%S A170195 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170195 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170195 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170195 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170195 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170195 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170195 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170195 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 A170195 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 A170195 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 A170195 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 A170195 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^39 -
%F A170195 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35 - 40*t^34 - 40*t^33 - 40*t^32 -
%F A170195 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 -
%F A170195 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 -
%F A170195 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 -
%F A170195 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 -
%F A170195 40*t^2 - 40*t + 1)
%t A170195 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-40 t^Range[38]]+ 820t^39+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 23 2012 *)
%K A170195 nonn
%O A170195 0,2
%A A170195 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009