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A170708 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170708 #25 Oct 10 2024 05:10:07
%S A170708 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A170708 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A170708 2576581829865418752,66991127576500887552,1741769316989023076352
%N A170708 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170708 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A170708 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170708 About the initial comment, first disagreement is at index 50 and the difference is 351. - _Vincenzo Librandi_, Dec 06 2012
%H A170708 Vincenzo Librandi, <a href="/A170708/b170708.txt">Table of n, a(n) for n = 0..200</a>
%H A170708 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A170708 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 + ,2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + ,2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + ,2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + ,2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + ,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 + ,2*t + 1)/(325*t^50 - 25*t^49 - 25*t^48 - 25*t^47 - 25*t^46 - 25*t^45 - ,25*t^44 - 25*t^43 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - ,25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - ,25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - ,25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - ,25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - ,25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - ,25*t + 1).
%t A170708 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-25 t^Range[49]] + 325 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%t A170708 coxG[{50,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 07 2019 *)
%K A170708 nonn
%O A170708 0,2
%A A170708 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009