cp's OEIS Frontend

A170170 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170170 #8 Nov 22 2016 15:48:50
%S A170170 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A170170 73014444032,1168231104512,18691697672192,299067162755072,
%U A170170 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592
%N A170170 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170170 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A170170 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170170 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).
%F A170170 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 A170170 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 A170170 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 A170170 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 A170170 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(120*t^39 -
%F A170170 15*t^38 - 15*t^37 - 15*t^36 - 15*t^35 - 15*t^34 - 15*t^33 - 15*t^32 -
%F A170170 15*t^31 - 15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 -
%F A170170 15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 -
%F A170170 15*t^17 - 15*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 -
%F A170170 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 -
%F A170170 15*t^2 - 15*t + 1)
%t A170170 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-15 t^Range[38]]+ 120t^39+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 19 2012 *)
%K A170170 nonn
%O A170170 0,2
%A A170170 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009