cp's OEIS Frontend

A170723 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170723 #16 Jun 26 2022 12:42:57
%S A170723 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170723 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170723 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170723 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170723 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170723 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170723 About the initial comment, first disagreement is at index 50 and the difference is 861.  - _Vincenzo Librandi_, Dec 06 2012
%H A170723 Vincenzo Librandi, <a href="/A170723/b170723.txt">Table of n, a(n) for n = 0..200</a>
%H A170723 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170723 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 A170723 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 A170723 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 A170723 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 A170723 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 A170723 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 A170723 2*t + 1)/(820*t^50 - 40*t^49 - 40*t^48 - 40*t^47 - 40*t^46 - 40*t^45 -
%F A170723 40*t^44 - 40*t^43 - 40*t^42 - 40*t^41 - 40*t^40 - 40*t^39 - 40*t^38 -
%F A170723 40*t^37 - 40*t^36 - 40*t^35 - 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 -
%F A170723 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 -
%F A170723 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 -
%F A170723 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 -
%F A170723 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 -
%F A170723 40*t + 1)
%t A170723 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-40  t^Range[49]] + 820 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170723 coxG[{50,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 26 2022 *)
%K A170723 nonn
%O A170723 0,2
%A A170723 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009