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A168722 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168722 #11 Nov 24 2016 13:14:38
%S A168722 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A168722 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A168722 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A168722 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168722 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A168722 First disagreement at index 17: a(17) = 8880866416083463795397098530, A170764(17) = 8880866416083463795397099520. - _Klaus Brockhaus_, Mar 28 2011
%C A168722 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168722 G. C. Greubel, <a href="/A168722/b168722.txt">Table of n, a(n) for n = 0..500</a>
%H A168722 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A168722 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)/(946*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%t A168722 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)/(946*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 06 2016 *)
%Y A168722 Cf. A170764 (G.f.: (1+x)/(1-44*x)).
%K A168722 nonn
%O A168722 0,2
%A A168722 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009