cp's OEIS Frontend

A170702 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170702 #9 Nov 19 2016 02:57:50
%S A170702 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170702 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170702 86016000000000000,1720320000000000000,34406400000000000000
%N A170702 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170702 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170702 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170702 About the initial comment, first disagreement is at index 50 and the difference is 210.  - _Vincenzo Librandi_, Dec 08 2012
%H A170702 Vincenzo Librandi, <a href="/A170702/b170702.txt">Table of n, a(n) for n = 0..200</a>
%H A170702 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A170702 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 A170702 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 A170702 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 A170702 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 A170702 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 A170702 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 A170702 2*t + 1)/(190*t^50 - 19*t^49 - 19*t^48 - 19*t^47 - 19*t^46 - 19*t^45 -
%F A170702 19*t^44 - 19*t^43 - 19*t^42 - 19*t^41 - 19*t^40 - 19*t^39 - 19*t^38 -
%F A170702 19*t^37 - 19*t^36 - 19*t^35 - 19*t^34 - 19*t^33 - 19*t^32 - 19*t^31 -
%F A170702 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 -
%F A170702 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 -
%F A170702 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 -
%F A170702 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 -
%F A170702 19*t + 1)
%t A170702 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-19 t^Range[49]] + 190t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 200}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170702 nonn
%O A170702 0,2
%A A170702 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009