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A170707 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170707 #23 Oct 10 2024 05:10:03
%S A170707 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A170707 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A170707 1549720764160156250,38743019104003906250,968575477600097656250
%N A170707 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170707 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A170707 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170707 About the initial comment, first disagreement is at index 50 and the difference is 325. - _Vincenzo Librandi_, Dec 06 2012
%H A170707 Vincenzo Librandi, <a href="/A170707/b170707.txt">Table of n, a(n) for n = 0..200</a>
%H A170707 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
%F A170707 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 A170707 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 A170707 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 A170707 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 A170707 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 A170707 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 A170707 2*t + 1)/(300*t^50 - 24*t^49 - 24*t^48 - 24*t^47 - 24*t^46 - 24*t^45 -
%F A170707 24*t^44 - 24*t^43 - 24*t^42 - 24*t^41 - 24*t^40 - 24*t^39 - 24*t^38 -
%F A170707 24*t^37 - 24*t^36 - 24*t^35 - 24*t^34 - 24*t^33 - 24*t^32 - 24*t^31 -
%F A170707 24*t^30 - 24*t^29 - 24*t^28 - 24*t^27 - 24*t^26 - 24*t^25 - 24*t^24 -
%F A170707 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 - 24*t^18 - 24*t^17 -
%F A170707 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 -
%F A170707 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 -
%F A170707 24*t + 1).
%t A170707 With[{num=Total[2 t^Range[49]] + t^50 + 1, den = Total[-24 t^Range[49]] + 300 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170707 coxG[{50,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 24 2016 *)
%K A170707 nonn
%O A170707 0,2
%A A170707 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009