A331714 Number of non-isomorphic set-systems with 3 sets each with n elements.

1, 5, 12, 25, 44, 73, 112, 166, 235, 325, 436, 575, 742, 945, 1184, 1468, 1797, 2181, 2620, 3125, 3696, 4345, 5072, 5890

Offset

1,2

Comments

a(n) is the number of nonequivalent binary matrices with 3 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..24.

Example

The a(2) = 5 set systems are:
  {{1,2}, {3,4}, {5,6}},
  {{1,2}, {1,3}, {4,5}},
  {{1,2}, {1,3}, {1,4}},
  {{1,2}, {1,3}, {2,4}},
  {{1,2}, {1,3}, {2,3}}.
.
These correspond to the following matrices:
  [1 0 0]  [1 1 0]  [1 1 1]  [1 1 0]  [1 1 0]
  [1 0 0]  [1 0 0]  [1 0 0]  [1 0 1]  [1 0 1]
  [0 1 0]  [0 1 0]  [0 1 0]  [0 1 0]  [0 1 1]
  [0 1 0]  [0 0 1]  [0 0 1]  [0 0 1]
  [0 0 1]  [0 0 1]
  [0 0 1]

Crossrefs

Column k=3 of A331508.

Cf. A331713.

Sequence in context: A336877 A212058 A303854 * A086168 A301748 A108201

Adjacent sequences: A331711 A331712 A331713 * A331715 A331716 A331717

Keyword

nonn,more

Author

Andrew Howroyd, Jan 31 2020

Status

approved