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A168718 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168718 #15 Nov 24 2016 13:13:18
%S A168718 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A168718 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A168718 17196646400000000000,687865856000000000000,27514634240000000000000
%N A168718 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168718 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A168718 First disagreement at index 17: a(17) = 1760936591359999999999999180, A170760(17) = 1760936591360000000000000000. - _Klaus Brockhaus_, Mar 28 2011
%C A168718 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168718 G. C. Greubel, <a href="/A168718/b168718.txt">Table of n, a(n) for n = 0..500</a>
%H A168718 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A168718 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)/(780*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
%t A168718 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)/(780*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 05 2016 *)
%t A168718 coxG[{17,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 10 2016 *)
%Y A168718 Cf. A170760 (G.f.: (1+x)/(1-40*x)).
%K A168718 nonn,easy
%O A168718 0,2
%A A168718 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009