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%I A170694 #12 Aug 11 2017 15:57:20
%S A170694 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A170694 67077144576,804925734912,9659108818944,115909305827328,
%U A170694 1390911669927936,16690940039135232,200291280469622784
%N A170694 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170694 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A170694 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170694 About the initial comment, first disagreement is at index 50 and the difference is 78. - _Vincenzo Librandi_, Dec 08 2012
%H A170694 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
%F A170694 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 A170694 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 A170694 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 A170694 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 A170694 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 A170694 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 A170694 2*t + 1)/(66*t^50 - 11*t^49 - 11*t^48 - 11*t^47 - 11*t^46 - 11*t^45 -
%F A170694 11*t^44 - 11*t^43 - 11*t^42 - 11*t^41 - 11*t^40 - 11*t^39 - 11*t^38 -
%F A170694 11*t^37 - 11*t^36 - 11*t^35 - 11*t^34 - 11*t^33 - 11*t^32 - 11*t^31 -
%F A170694 11*t^30 - 11*t^29 - 11*t^28 - 11*t^27 - 11*t^26 - 11*t^25 - 11*t^24 -
%F A170694 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 - 11*t^18 - 11*t^17 -
%F A170694 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 -
%F A170694 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 -
%F A170694 11*t + 1)
%t A170694 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-11 t^Range[49]] + 66 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170694 coxG[{50,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 11 2017 *)
%K A170694 nonn
%O A170694 0,2
%A A170694 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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