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A170686 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170686 #12 Nov 21 2016 10:36:50
%S A170686 1,5,20,80,320,1280,5120,20480,81920,327680,1310720,5242880,20971520,
%T A170686 83886080,335544320,1342177280,5368709120,21474836480,85899345920,
%U A170686 343597383680,1374389534720,5497558138880,21990232555520,87960930222080
%N A170686 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170686 The initial terms coincide with those of A003947, although the two sequences are eventually different.
%C A170686 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170686 About the initial comment, first disagreement is at index 50 and the difference is 10.  - _Vincenzo Librandi_, Dec 09 2012
%H A170686 Vincenzo Librandi, <a href="/A170686/b170686.txt">Table of n, a(n) for n = 0..200</a>
%H A170686 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -6).
%F A170686 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 A170686 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 A170686 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 A170686 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 A170686 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 A170686 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 A170686 2*t + 1)/(6*t^50 - 3*t^49 - 3*t^48 - 3*t^47 - 3*t^46 - 3*t^45 - 3*t^44 -
%F A170686 3*t^43 - 3*t^42 - 3*t^41 - 3*t^40 - 3*t^39 - 3*t^38 - 3*t^37 - 3*t^36 -
%F A170686 3*t^35 - 3*t^34 - 3*t^33 - 3*t^32 - 3*t^31 - 3*t^30 - 3*t^29 - 3*t^28 -
%F A170686 3*t^27 - 3*t^26 - 3*t^25 - 3*t^24 - 3*t^23 - 3*t^22 - 3*t^21 - 3*t^20 -
%F A170686 3*t^19 - 3*t^18 - 3*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 -
%F A170686 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3
%F A170686 - 3*t^2 - 3*t + 1).
%t A170686 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-3 t^Range[49]] + 6 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* _Vincenzo Librandi_, Dec 09 2012 *)
%K A170686 nonn
%O A170686 0,2
%A A170686 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009