cp's OEIS Frontend

A170701 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170701 #9 Nov 19 2016 02:59:15
%S A170701 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,
%T A170701 339671260820,6453753955580,122621325156020,2329805177964380,
%U A170701 44266298381323220,841059669245141180,15980133715657682420
%N A170701 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170701 The initial terms coincide with those of A170739, although the two sequences are eventually different.
%C A170701 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170701 About the initial comment, first disagreement is at index 50 and the difference is 190.  - _Vincenzo Librandi_, Dec 08 2012
%H A170701 Vincenzo Librandi, <a href="/A170701/b170701.txt">Table of n, a(n) for n = 0..200</a>
%H A170701 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).
%F A170701 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 A170701 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 A170701 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 A170701 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 A170701 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 A170701 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 A170701 2*t + 1)/(171*t^50 - 18*t^49 - 18*t^48 - 18*t^47 - 18*t^46 - 18*t^45 -
%F A170701 18*t^44 - 18*t^43 - 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 -
%F A170701 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 -
%F A170701 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 -
%F A170701 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 -
%F A170701 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 -
%F A170701 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 -
%F A170701 18*t + 1)
%t A170701 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-18 t^Range[49]] + 171t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170701 nonn
%O A170701 0,2
%A A170701 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009