cp's OEIS Frontend

A170693 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170693 #15 Feb 28 2018 11:31:20
%S A170693 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A170693 28295372292,311249095212,3423740047332,37661140520652,
%U A170693 414272545727172,4556998002998892,50126978032987812,551396758362865932
%N A170693 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170693 The initial terms coincide with those of A003954, although the two sequences are eventually different.
%C A170693 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170693 About the initial comment, first disagreement is at index 50 and the difference is 66. - _Vincenzo Librandi_, Dec 08 2012
%H A170693 Vincenzo Librandi, <a href="/A170693/b170693.txt">Table of n, a(n) for n = 0..200</a>
%H A170693 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).
%F A170693 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 A170693 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 A170693 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 A170693 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 A170693 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 A170693 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 A170693 2*t + 1)/(55*t^50 - 10*t^49 - 10*t^48 - 10*t^47 - 10*t^46 - 10*t^45 -
%F A170693 10*t^44 - 10*t^43 - 10*t^42 - 10*t^41 - 10*t^40 - 10*t^39 - 10*t^38 -
%F A170693 10*t^37 - 10*t^36 - 10*t^35 - 10*t^34 - 10*t^33 - 10*t^32 - 10*t^31 -
%F A170693 10*t^30 - 10*t^29 - 10*t^28 - 10*t^27 - 10*t^26 - 10*t^25 - 10*t^24 -
%F A170693 10*t^23 - 10*t^22 - 10*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 -
%F A170693 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 -
%F A170693 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 -
%F A170693 10*t + 1)
%t A170693 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-10 t^Range[49]] + 55 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170693 coxG[{50,55,-10}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 04 2015 *)
%K A170693 nonn
%O A170693 0,2
%A A170693 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009