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Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
0

%I #7 Jul 10 2020 15:20:18

%S 1,20,380,7030,129960,2400840,44352270,819332820,15135787980,

%T 279607936230,5165281123560,95419783331640,1762718203098270,

%U 32563220683609620,601550117011031580,11112615265773737430

%N Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

%C The initial terms coincide with those of A170739, 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 (18, 18, -171).

%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(171*t^3 - 18*t^2 - 18*t + 1)

%t coxG[{3,171,-18}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 10 2020 *)

%K nonn

%O 0,2

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