cp's OEIS Frontend

A170710 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170710 #18 Nov 19 2016 02:38:31
%S A170710 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A170710 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A170710 6734329687587160064,188561231252440481792,5279714475068333490176
%N A170710 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170710 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A170710 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170710 About the initial comment, first disagreement is at index 50 and the difference is 406. [_Vincenzo Librandi_, Dec 06 2012]
%H A170710 Vincenzo Librandi, <a href="/A170710/b170710.txt">Table of n, a(n) for n = 0..200</a>
%H A170710 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A170710 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 A170710 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 A170710 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 A170710 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 A170710 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 A170710 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 A170710 2*t + 1)/(378*t^50 - 27*t^49 - 27*t^48 - 27*t^47 - 27*t^46 - 27*t^45 -
%F A170710 27*t^44 - 27*t^43 - 27*t^42 - 27*t^41 - 27*t^40 - 27*t^39 - 27*t^38 -
%F A170710 27*t^37 - 27*t^36 - 27*t^35 - 27*t^34 - 27*t^33 - 27*t^32 - 27*t^31 -
%F A170710 27*t^30 - 27*t^29 - 27*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 -
%F A170710 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 -
%F A170710 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 -
%F A170710 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 -
%F A170710 27*t + 1).
%t A170710 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-27t^Range[49]]+378t^50+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 20 2012 *)
%K A170710 nonn
%O A170710 0,2
%A A170710 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009