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Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
0

%I #8 Mar 23 2020 07:07:25

%S 1,27,702,18252,474201,12320100,320085675,8316067500,216057716550,

%T 5613342710625,145838884522500,3789004401804375,98441196968058750,

%U 2557576669978687500,66447774146243953125,1726363373899181062500

%N Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A170746, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (25,25,25,-325).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

%o (PARI) Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^4 - 25*t^3 - 25*t^2 - 25*t + 1) + O(t^20)) \\ _Jinyuan Wang_, Mar 23 2020

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009