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A170704 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170704 #11 Jul 10 2017 20:14:05
%S A170704 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170704 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170704 295665060514131968,6504631331310903296,143101889288839872512
%N A170704 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170704 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170704 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170704 About the initial comment, first disagreement is at index 50 and the difference is 253.  - _Vincenzo Librandi_, Dec 08 2012
%H A170704 Vincenzo Librandi, <a href="/A170704/b170704.txt">Table of n, a(n) for n = 0..200</a>
%H A170704 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A170704 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 A170704 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 A170704 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 A170704 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 A170704 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 A170704 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 A170704 2*t + 1)/(231*t^50 - 21*t^49 - 21*t^48 - 21*t^47 - 21*t^46 - 21*t^45 -
%F A170704 21*t^44 - 21*t^43 - 21*t^42 - 21*t^41 - 21*t^40 - 21*t^39 - 21*t^38 -
%F A170704 21*t^37 - 21*t^36 - 21*t^35 - 21*t^34 - 21*t^33 - 21*t^32 - 21*t^31 -
%F A170704 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 -
%F A170704 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 -
%F A170704 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 -
%F A170704 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 -
%F A170704 21*t + 1)
%t A170704 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-21 t^Range[49]] + 231t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170704 coxG[{50,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 10 2017 *)
%K A170704 nonn
%O A170704 0,2
%A A170704 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009