cp's OEIS Frontend

A168693 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168693 #16 Jul 05 2017 19:20:10
%S A168693 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,
%T A168693 615093750000,9226406250000,138396093750000,2075941406250000,
%U A168693 31139121093750000,467086816406250000,7006302246093750000
%N A168693 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168693 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A168693 First disagreement at index 17: a(17) = 105094533691406249880, A170735(17) = 105094533691406250000. - _Klaus Brockhaus_, Mar 30 2011
%C A168693 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168693 G. C. Greubel, <a href="/A168693/b168693.txt">Table of n, a(n) for n = 0..500</a>
%H A168693 <a href="/index/Rec#order_17">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, -105).
%F A168693 G.f.: (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^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 A168693 CoefficientList[Series[(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^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,0,50}], t] (* _G. C. Greubel_, Aug 03 2016 *)
%t A168693 coxG[{17,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 05 2017 *)
%Y A168693 Cf. A170735 (G.f.: (1+x)/(1-15*x)).
%K A168693 nonn
%O A168693 0,2
%A A168693 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009