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A168713 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168713 #13 Oct 09 2018 19:42:45
%S A168713 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A168713 2316214687500,81067514062500,2837362992187500,99307704726562500,
%U A168713 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500
%N A168713 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168713 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A168713 First disagreement at index 17: a(17) = 182553939896489868164061870, A170755(17) = 182553939896489868164062500. - _Klaus Brockhaus_, Mar 28 2011
%C A168713 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168713 G. C. Greubel, <a href="/A168713/b168713.txt">Table of n, a(n) for n = 0..500</a>
%H A168713 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
%F A168713 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)/(595*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
%t A168713 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)/(595*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 05 2016 *)
%t A168713 coxG[{17,595,-34}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 09 2018 *)
%Y A168713 Cf. A170755 (G.f.: (1+x)/(1-35*x)).
%K A168713 nonn
%O A168713 0,2
%A A168713 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009