cp's OEIS Frontend

A169317 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169317 #12 May 10 2018 01:21:58
%S A169317 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A169317 615093750000,9226406250000,138396093750000,2075941406250000,
%U A169317 31139121093750000,467086816406250000,7006302246093750000
%N A169317 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169317 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A169317 First disagreement at index 30: a(30) = 204534463181743025779724121093749880, A170735(30) = 204534463181743025779724121093750000. - _Klaus Brockhaus_, Jun 22 2011
%C A169317 Computed with Magma using commands similar to those used to compute A154638.
%H A169317 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).
%F A169317 G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(105*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
%t A169317 With[{num=Total[2t^Range[29]]+t^30+1,den=Total[-14 t^Range[29]]+ 105t^30+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Feb 21 2013 *)
%Y A169317 Cf. A170735 (G.f.: (1+x)/(1-15*x)).
%K A169317 nonn
%O A169317 0,2
%A A169317 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009