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A170691 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170691 #15 Feb 14 2018 14:58:05
%S A170691 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A170691 34867844010,313810596090,2824295364810,25418658283290,
%U A170691 228767924549610,2058911320946490,18530201888518410,166771816996665690
%N A170691 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170691 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A170691 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170691 About the initial comment, first disagreement is at index 50 and the difference is 45. - _Vincenzo Librandi_, Dec 08 2012
%H A170691 Vincenzo Librandi, <a href="/A170691/b170691.txt">Table of n, a(n) for n = 0..200</a>
%H A170691 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).
%F A170691 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 A170691 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 A170691 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 A170691 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 A170691 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 A170691 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 A170691 2*t + 1)/(36*t^50 - 8*t^49 - 8*t^48 - 8*t^47 - 8*t^46 - 8*t^45 - 8*t^44
%F A170691 - 8*t^43 - 8*t^42 - 8*t^41 - 8*t^40 - 8*t^39 - 8*t^38 - 8*t^37 - 8*t^36
%F A170691 - 8*t^35 - 8*t^34 - 8*t^33 - 8*t^32 - 8*t^31 - 8*t^30 - 8*t^29 - 8*t^28
%F A170691 - 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 - 8*t^22 - 8*t^21 - 8*t^20
%F A170691 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12
%F A170691 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 -
%F A170691 8*t^3 - 8*t^2 - 8*t + 1).
%t A170691 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-8 t^Range[49]]+ 36 t^50+1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 11 2012 *)
%K A170691 nonn
%O A170691 0,2
%A A170691 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009