cp's OEIS Frontend

A170724 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170724 #14 Nov 18 2016 17:41:45
%S A170724 1,43,1806,75852,3185784,133802928,5619722976,236028364992,
%T A170724 9913191329664,416354035845888,17486869505527296,734448519232146432,
%U A170724 30846837807750150144,1295567187925506306048,54413821892871264854016
%N A170724 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170724 The initial terms coincide with those of A170762, although the two sequences are eventually different.
%C A170724 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170724 About the initial comment, first disagreement is at index 50 and the difference is 903.  - _Vincenzo Librandi_, Dec 07 2012
%H A170724 Vincenzo Librandi, <a href="/A170724/b170724.txt">Table of n, a(n) for n = 0..200</a>
%H A170724 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).
%F A170724 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 A170724 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 A170724 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 A170724 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 A170724 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 A170724 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 A170724 2*t + 1)/(861*t^50 - 41*t^49 - 41*t^48 - 41*t^47 - 41*t^46 - 41*t^45 -
%F A170724 41*t^44 - 41*t^43 - 41*t^42 - 41*t^41 - 41*t^40 - 41*t^39 - 41*t^38 -
%F A170724 41*t^37 - 41*t^36 - 41*t^35 - 41*t^34 - 41*t^33 - 41*t^32 - 41*t^31 -
%F A170724 41*t^30 - 41*t^29 - 41*t^28 - 41*t^27 - 41*t^26 - 41*t^25 - 41*t^24 -
%F A170724 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 - 41*t^17 -
%F A170724 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 -
%F A170724 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 -
%F A170724 41*t + 1)
%t A170724 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-41 t^Range[49]] + 861 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 07 2012 *)
%K A170724 nonn
%O A170724 0,2
%A A170724 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009