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A169206 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

%I A169206 #12 May 10 2018 02:16:52
%S A169206 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A169206 28766348771328,1380784741023744,66277667569139712,
%U A169206 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A169206 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
%C A169206 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A169206 First disagreement at index 27: a(27) = 2526203030497011773442208333908656746383014760, A170768(27) = 2526203030497011773442208333908656746383015936. - _Klaus Brockhaus_, May 07 2011
%C A169206 Computed with Magma using commands similar to those used to compute A154638.
%H A169206 <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).
%F A169206 G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*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)/(1128*t^27 - 47*t^26 - 47*t^25 - 47*t^24 - 47*t^23 - 47*t^22 - 47*t^21 - 47*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
%t A169206 coxG[{27,1128,-47}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 25 2017 *)
%Y A169206 Cf. A170768 (G.f.: (1+x)/(1-48*x)).
%K A169206 nonn
%O A169206 0,2
%A A169206 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009