cp's OEIS Frontend

A170703 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170703 #9 Nov 19 2016 02:56:24
%S A170703 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A170703 832102905942,17474161024782,366957381520422,7706105011928862,
%U A170703 161828205250506102,3398392310260628142,71366238515473190982
%N A170703 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170703 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A170703 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170703 About the initial comment, first disagreement is at index 50 and the difference is 231.  - _Vincenzo Librandi_, Dec 08 2012
%H A170703 Vincenzo Librandi, <a href="/A170703/b170703.txt">Table of n, a(n) for n = 0..200</a>
%H A170703 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A170703 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 A170703 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 A170703 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 A170703 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 A170703 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 A170703 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 A170703 2*t + 1)/(210*t^50 - 20*t^49 - 20*t^48 - 20*t^47 - 20*t^46 - 20*t^45 -
%F A170703 20*t^44 - 20*t^43 - 20*t^42 - 20*t^41 - 20*t^40 - 20*t^39 - 20*t^38 -
%F A170703 20*t^37 - 20*t^36 - 20*t^35 - 20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 -
%F A170703 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 -
%F A170703 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 -
%F A170703 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 -
%F A170703 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 -
%F A170703 20*t + 1)
%t A170703 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-20 t^Range[49]] + 210t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%K A170703 nonn
%O A170703 0,2
%A A170703 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009