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A170727 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170727 #15 Apr 14 2022 14:54:31
%S A170727 1,46,2070,93150,4191750,188628750,8488293750,381973218750,
%T A170727 17188794843750,773495767968750,34807309558593750,1566328930136718750,
%U A170727 70484801856152343750,3171816083526855468750,142731723758708496093750
%N A170727 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170727 The initial terms coincide with those of A170765, although the two sequences are eventually different.
%C A170727 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170727 About the initial comment, first disagreement is at index 50 and the difference is 1035.  - _Vincenzo Librandi_, Dec 08 2012
%H A170727 Vincenzo Librandi, <a href="/A170727/b170727.txt">Table of n, a(n) for n = 0..200</a>
%H A170727 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).
%F A170727 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 +
%F A170727 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170727 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170727 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170727 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170727 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 +
%F A170727 2*t + 1)/(990*t^50 - 44*t^49 - 44*t^48 - 44*t^47 - 44*t^46 - 44*t^45 -
%F A170727 44*t^44 - 44*t^43 - 44*t^42 - 44*t^41 - 44*t^40 - 44*t^39 - 44*t^38 -
%F A170727 44*t^37 - 44*t^36 - 44*t^35 - 44*t^34 - 44*t^33 - 44*t^32 - 44*t^31 -
%F A170727 44*t^30 - 44*t^29 - 44*t^28 - 44*t^27 - 44*t^26 - 44*t^25 - 44*t^24 -
%F A170727 44*t^23 - 44*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 -
%F A170727 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 -
%F A170727 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 -
%F A170727 44*t + 1).
%F A170727 From _Zak Seidov_, Dec 04 2009: (Start)
%F A170727 G.f.: (t^50+2f+1)/(990*t^50-44f+1) with f=t*(1+t+t^2+t^3+t^4+t^5+t^6)*(1+t^7+t^14+t^21+t^28+t^35+t^42).
%F A170727 G.f.: (1 + t - t^50 - t^51)/(1 - 45*t + 1034*t^50 - 990*t^51).
%F A170727 (End)
%t A170727 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-44 t^Range[49]] + 990t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170727 coxG[{50,990,-44}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 14 2022 *)
%K A170727 nonn
%O A170727 0,2
%A A170727 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009