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%I #9 Nov 24 2016 10:50:21
%S 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U 6734329687587160064,188561231252440481386,5279714475068333467440
%N Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
%C The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A167285/b167285.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F G.f.: (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^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 CoefficientList[Series[(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^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_, Jun 05 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009