cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-12 of 12 results.

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

Original entry on oeis.org

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

Views

Author

Andrew Howroyd, Jan 31 2020

Keywords

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.

Examples

			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.

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

Original entry on oeis.org

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

Views

Author

Andrew Howroyd, Jan 31 2020

Keywords

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.

Examples

			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.
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.