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Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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%I #7 Mar 13 2018 12:18:23

%S 1,7,42,252,1491,8820,52185,308700,1826160,10802925,63906150,

%T 378045675,2236381350,13229622000,78261652875,462967596000,

%U 2738748634125,16201445085000,95841881782500,566965863568125,3353964722666250

%N Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%C The initial terms coincide with those of A003949, 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 (5, 5, 5, -15).

%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^4 - 5*t^3 - 5*t^2 - 5*t + 1)

%t coxG[{4,15,-5}] (* The coxG program is at A169452 *) (* or *) LinearRecurrence[ {5,5,5,-15},{1,7,42,252,1491},30] (* _Harvey P. Dale_, Mar 13 2018 *)

%K nonn

%O 0,2

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