A373723 Number of strictly totally positive 3 X 3 matrices having all terms in {1,...,n}.

0, 0, 22, 597, 7178, 43090, 207494

Offset

1,3

Comments

A matrix is strictly totally positive if all its minors are greater than zero.

Links

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

Mathematica

ispositive1[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], ispositive1[#]&], {n, 1, 7}]

Crossrefs

Cf. A211059, A373724.

Sequence in context: A240337 A084271 A092086 * A369142 A218478 A223624

Adjacent sequences: A373720 A373721 A373722 * A373724 A373725 A373726

Keyword

nonn,more

Author

José María Grau Ribas, Jun 15 2024

Status

approved