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A168764 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%I A168764 #16 Jan 28 2020 19:22:09
%S A168764 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A168764 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A168764 9304309958718547968,353563778431304822784,13435423580389583265792
%N A168764 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
%C A168764 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A168764 First disagreement at index 18: a(18) = 28014685382719214092500466971, A170758(18) = 28014685382719214092500467712. - _Klaus Brockhaus_, Mar 26 2011
%C A168764 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168764 G. C. Greubel, <a href="/A168764/b168764.txt">Table of n, a(n) for n = 0..500</a>
%H A168764 <a href="/index/Rec#order_18">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, 37, -703).
%F A168764 G.f.: (t^18 + 2*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^18 - 37*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 A168764 CoefficientList[Series[(t^18 + 2*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^18 - 37*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 11 2016 *)
%t A168764 coxG[{18,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 28 2020 *)
%Y A168764 Cf. A170758 (G.f.: (1+x)/(1-38*x)).
%K A168764 nonn,easy
%O A168764 0,2
%A A168764 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009