cp's OEIS Frontend

A170705 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170705 #11 Dec 31 2016 12:53:42
%S A170705 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170705 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170705 525950986368487704,12096872686475217192,278228071788929995416
%N A170705 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170705 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170705 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170705 About the initial comment, first disagreement is at index 50 and the difference is 276.  - _Vincenzo Librandi_, Dec 08 2012
%H A170705 Vincenzo Librandi, <a href="/A170705/b170705.txt">Table of n, a(n) for n = 0..200</a>
%H A170705 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A170705 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 A170705 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 A170705 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 A170705 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 A170705 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 A170705 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 A170705 2*t + 1)/(253*t^50 - 22*t^49 - 22*t^48 - 22*t^47 - 22*t^46 - 22*t^45 -
%F A170705 22*t^44 - 22*t^43 - 22*t^42 - 22*t^41 - 22*t^40 - 22*t^39 - 22*t^38 -
%F A170705 22*t^37 - 22*t^36 - 22*t^35 - 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 -
%F A170705 22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 -
%F A170705 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 -
%F A170705 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 -
%F A170705 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 -
%F A170705 22*t + 1)
%t A170705 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-22 t^Range[49]] + 253t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 200}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170705 coxG[{50,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 31 2016 *)
%K A170705 nonn
%O A170705 0,2
%A A170705 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009