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A168721 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168721 #13 Nov 24 2016 13:14:17
%S A168721 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A168721 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A168721 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A168721 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168721 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A168721 First disagreement at index 17: a(17) = 6011017132089732112341867898, A170763(17) = 6011017132089732112341868844. - _Klaus Brockhaus_, Mar 28 2011
%C A168721 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168721 G. C. Greubel, <a href="/A168721/b168721.txt">Table of n, a(n) for n = 0..500</a>
%H A168721 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A168721 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)/(903*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%t A168721 coxG[{17,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 27 2015 *)
%t A168721 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)/(903*t^17 - 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 06 2016 *)
%Y A168721 Cf. A170763 (G.f.: (1+x)/(1-43*x)).
%K A168721 nonn
%O A168721 0,2
%A A168721 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009