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A168716 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168716 #13 Sep 28 2021 17:07:15
%S A168716 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A168716 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A168716 9304309958718547968,353563778431304822784,13435423580389583265792
%N A168716 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168716 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A168716 First disagreement at index 17: a(17) = 737228562703137212960537883, A170758(17) = 737228562703137212960538624. - _Klaus Brockhaus_, Mar 28 2011
%C A168716 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168716 G. C. Greubel, <a href="/A168716/b168716.txt">Table of n, a(n) for n = 0..500</a>
%H A168716 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A168716 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)/(703*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
%t A168716 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 +
%t A168716 2*t^2 + 2*t + 1)/(703*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 05 2016 *)
%t A168716 coxG[{17,703,-37}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Sep 28 2021 *)
%Y A168716 Cf. A170758 (G.f.: (1+x)/(1-38*x)).
%K A168716 nonn
%O A168716 0,2
%A A168716 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009