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A170695 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170695 #13 Sep 26 2017 12:32:14
%S A170695 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T A170695 148462991222,1930018885886,25090245516518,326173191714734,
%U A170695 4240251492291542,55123269399790046,716602502197270598
%N A170695 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170695 The initial terms coincide with those of A170733, although the two sequences are eventually different.
%C A170695 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170695 About the initial comment, first disagreement is at index 50 and the difference is 91. - _Vincenzo Librandi_, Dec 08 2012
%H A170695 Vincenzo Librandi, <a href="/A170695/b170695.txt">Table of n, a(n) for n = 0..200</a>
%H A170695 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
%F A170695 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 A170695 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 A170695 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 A170695 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 A170695 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 A170695 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 A170695 2*t + 1)/(78*t^50 - 12*t^49 - 12*t^48 - 12*t^47 - 12*t^46 - 12*t^45 -
%F A170695 12*t^44 - 12*t^43 - 12*t^42 - 12*t^41 - 12*t^40 - 12*t^39 - 12*t^38 -
%F A170695 12*t^37 - 12*t^36 - 12*t^35 - 12*t^34 - 12*t^33 - 12*t^32 - 12*t^31 -
%F A170695 12*t^30 - 12*t^29 - 12*t^28 - 12*t^27 - 12*t^26 - 12*t^25 - 12*t^24 -
%F A170695 12*t^23 - 12*t^22 - 12*t^21 - 12*t^20 - 12*t^19 - 12*t^18 - 12*t^17 -
%F A170695 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 -
%F A170695 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 -
%F A170695 12*t + 1)
%t A170695 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-12 t^Range[49]] + 78 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170695 coxG[{50, 78, -12}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 26 2017 *)
%K A170695 nonn
%O A170695 0,2
%A A170695 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009