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A168695 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168695 #12 Nov 24 2016 13:04:01
%S A168695 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A168695 125563633938,2134581776946,36287890208082,616894133537394,
%U A168695 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A168695 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168695 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A168695 First disagreement at index 17: a(17) = 875901453762003632505, A170737(17) = 875901453762003632658. - _Klaus Brockhaus_, Mar 30 2011
%C A168695 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168695 G. C. Greubel, <a href="/A168695/b168695.txt">Table of n, a(n) for n = 0..500</a>
%H A168695 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A168695 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)/ (136*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%t A168695 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)/(136*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 03 2016 *)
%Y A168695 Cf. A170737 (G.f.: (1+x)/(1-17*x)).
%K A168695 nonn
%O A168695 0,2
%A A168695 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009