A331715 Number of non-isomorphic set-systems with 4 sets each with n elements.

1, 11, 66, 278, 966, 2957, 8149, 20676, 48911, 108942, 230201, 464528, 899633, 1679685, 3034620

Offset

1,2

Comments

a(n) is the number of nonequivalent binary matrices with 4 distinct columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.

Links

Table of n, a(n) for n=1..15.

Example

The a(2) = 11 matrices are:
  [1 0 0 0]  [1 1 0 0]  [1 1 1 0]  [1 1 0 0]  [1 1 0 0]
  [1 0 0 0]  [1 0 0 0]  [1 0 0 0]  [1 0 1 0]  [1 0 0 0]
  [0 1 0 0]  [0 1 0 0]  [0 1 0 0]  [0 1 0 0]  [0 1 0 0]
  [0 1 0 0]  [0 0 1 0]  [0 0 1 0]  [0 0 1 0]  [0 0 1 1]
  [0 0 1 0]  [0 0 1 0]  [0 0 0 1]  [0 0 0 1]  [0 0 1 0]
  [0 0 1 0]  [0 0 0 1]  [0 0 0 1]  [0 0 0 1]  [0 0 0 1]
  [0 0 0 1]  [0 0 0 1]
  [0 0 0 1]
.
  [1 1 1 1]  [1 1 1 0]  [1 1 0 0]  [1 1 0 0]  [1 1 0 1]  [1 1 0 0]
  [1 0 0 0]  [1 0 0 1]  [1 0 1 0]  [1 0 1 0]  [1 0 1 0]  [1 0 1 0]
  [0 1 0 0]  [0 1 0 0]  [0 1 1 0]  [0 1 0 1]  [0 1 1 0]  [0 1 0 1]
  [0 0 1 0]  [0 0 1 0]  [0 0 0 1]  [0 0 1 0]  [0 0 0 1]  [0 0 1 1]
  [0 0 0 1]  [0 0 0 1]  [0 0 0 1]  [0 0 0 1]
.
A set system corresponding to the first of these is {{1,2}, {3,4}, {5,6}, {7,8}}.

Crossrefs

Column k=4 of A331508.

Cf. A331714.

Sequence in context: A154617 A297751 A063842 * A162628 A247610 A008503

Adjacent sequences: A331712 A331713 A331714 * A331716 A331717 A331718

Keyword

nonn,more

Author

Andrew Howroyd, Jan 31 2020

Status

approved