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A170730 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170730 #9 Nov 18 2016 17:26:02
%S A170730 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A170730 28766348771328,1380784741023744,66277667569139712,
%U A170730 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A170730 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170730 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A170730 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170730 About the initial comment, first disagreement is at index 50 and the difference is 1176.  - _Vincenzo Librandi_, Dec 08 2012
%H A170730 Vincenzo Librandi, <a href="/A170730/b170730.txt">Table of n, a(n) for n = 0..200</a>
%H A170730 <a href="/index/Rec#order_50">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, 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 A170730 G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*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^50 - 47*t^49 - 47*t^48 - 47*t^47 - 47*t^46 - 47*t^45 - 47*t^44 - 47*t^43 - 47*t^42 - 47*t^41 - 47*t^40 - 47*t^39 - 47*t^38 - 47*t^37 - 47*t^36 - 47*t^35 - 47*t^34 - 47*t^33 - 47*t^32 - 47*t^31 - 47*t^30 - 47*t^29 - 47*t^28 - 47*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 A170730 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-47 t^Range[49]] + 1128t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 200}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170730 nonn
%O A170730 0,2
%A A170730 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009