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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)^3 = I.
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%I #7 Oct 02 2021 17:22:56

%S 1,7,42,231,1260,6825,36960,200025,1082550,5858475,31704750,171577875,

%T 928536000,5024998125,27194002500,147166963125,796429856250,

%U 4310074059375,23325015131250,126228998109375,683118955312500

%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)^3 = 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_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, -15).

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

%t coxG[{3,15,-5}] (* The coxG program is at A169452 *) (* or *) LinearRecurrence[{5,5,-15},{1,7,42,231},30] (* _Harvey P. Dale_, Oct 02 2021 *)

%K nonn

%O 0,2

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