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Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
0

%I #9 Feb 22 2024 13:33:38

%S 1,16,240,3600,54000,810000,12150000,182249880,2733746400,41006169120,

%T 615092133600,9226375956000,138395548620000,2075931868500000,

%U 31138957615514280,467084058053130000,7006256278106196720

%N Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

%C The initial terms coincide with those of A170735, 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_07">Index entries for linear recurrences with constant coefficients</a>, signature (14,14,14,14,14,14,-105).

%F G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

%K nonn

%O 0,2

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