A380630 Number of matrices with n columns, any number of distinct rows and entries in 0..2 and without an all zero row up to permutations of rows and columns.

1, 4, 144, 11250688, 50371911404609819639808, 58894902159279477652776826941706227937004584169809397602591562463707136

Offset: 0

Author

Andrew Howroyd, Feb 19 2025

Keywords

• nonn

Comments

The matrices can be regarded as sets of n-tuples. Equivalence is up to simultaneous permutations of the tuples.

Another interpretation as the number of non-isomorphic formulas in conjunctive normal form is described in A380610.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..7

Crossrefs

Row sums of A380610.

Cf. A003180, A380518.

Programs

PARI

\\ Fix, permcount defined in A380610.
a(n)={my(s=0); forpart(q=n, s+=permcount(q)*Fix(q, 1)); s/n!/2}