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%I #13 Jul 07 2024 13:06:33
%S 1,61,797,6490,32744,146441,492277
%N Number of totally positive 3 X 3 matrices having all terms in {1,...,n}.
%C A matrix is totally positive if all its minors are nonnegative.
%t ispositive2[M_]:=ispositive1[M]=Union@Table[Select[Union@Flatten@Minors[M,r],(#<= 0)&]=={},{r,1,Length[M]}]=={True};
%t W[n_]:=W[n]=Flatten[Table[{{a11,a12,a13},{a21,a22,a23},{a31,a32,a33}},{a11,1,n},{a12,1,n},{a13,1,n},{a21,1,n},{a22,1,n},{a23,1,n},{a31,1,n},{a32,1,n},{a33,1,n}],8];
%t Table[Length@Select[W[n],ispositive2[#]&],{n,1,6}]
%Y Cf. A211059, A373723.
%K nonn,more
%O 1,2
%A _José María Grau Ribas_, Jun 15 2024
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