A373724 Number of totally positive 3 X 3 matrices having all terms in {1,...,n}.

1, 61, 797, 6490, 32744, 146441, 492277

Offset

1,2

Comments

A matrix is totally positive if all its minors are nonnegative.

Links

Table of n, a(n) for n=1..7.

Mathematica

ispositive2[M_]:=ispositive1[M]=Union@Table[Select[Union@Flatten@Minors[M, r], (#<= 0)&]=={}, {r, 1, Length[M]}]=={True};
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];
Table[Length@Select[W[n], ispositive2[#]&], {n, 1, 6}]

Crossrefs

Cf. A211059, A373723.

Sequence in context: A372963 A251426 A232858 * A093473 A000506 A008358

Adjacent sequences: A373721 A373722 A373723 * A373725 A373726 A373727

Keyword

nonn,more

Author

José María Grau Ribas, Jun 15 2024

Status

approved