cp's OEIS Frontend

A170692 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170692 #13 Nov 21 2016 10:40:41
%S A170692 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,
%T A170692 11000000000,110000000000,1100000000000,11000000000000,
%U A170692 110000000000000,1100000000000000,11000000000000000,110000000000000000
%N A170692 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170692 The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C A170692 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170692 About the initial comment, first disagreement is at index 50 and the difference is 55. - _Vincenzo Librandi_, Dec 08 2012
%H A170692 Vincenzo Librandi, <a href="/A170692/b170692.txt">Table of n, a(n) for n = 0..200</a>
%H A170692 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).
%F A170692 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 A170692 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 A170692 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 A170692 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 A170692 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 A170692 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 A170692 2*t + 1)/(45*t^50 - 9*t^49 - 9*t^48 - 9*t^47 - 9*t^46 - 9*t^45 - 9*t^44
%F A170692 - 9*t^43 - 9*t^42 - 9*t^41 - 9*t^40 - 9*t^39 - 9*t^38 - 9*t^37 - 9*t^36
%F A170692 - 9*t^35 - 9*t^34 - 9*t^33 - 9*t^32 - 9*t^31 - 9*t^30 - 9*t^29 - 9*t^28
%F A170692 - 9*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20
%F A170692 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12
%F A170692 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 -
%F A170692 9*t^3 - 9*t^2 - 9*t + 1)
%t A170692 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-9 t^Range[49]]+ 45 t^50+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 20 2011 *)
%K A170692 nonn
%O A170692 0,2
%A A170692 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009