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A168706 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%I A168706 #13 Sep 06 2020 19:50:21
%S A168706 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A168706 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A168706 6734329687587160064,188561231252440481792,5279714475068333490176
%N A168706 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
%C A168706 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A168706 First disagreement at index 17: a(17) = 4139296148453573456297578, A170748(17) = 4139296148453573456297984. - _Klaus Brockhaus_, Mar 30 2011
%C A168706 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168706 G. C. Greubel, <a href="/A168706/b168706.txt">Table of n, a(n) for n = 0..500</a>
%H A168706 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A168706 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)/(378*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
%t A168706 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)/(378*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)
%t A168706 coxG[{17,378,-27}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 06 2020 *)
%Y A168706 Cf. A170748 (G.f.: (1+x)/(1-28*x)).
%K A168706 nonn
%O A168706 0,2
%A A168706 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009