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.

Showing 1-3 of 3 results.

A305999 Number of unlabeled spanning intersecting set-systems on n vertices with no singletons.

Original entry on oeis.org

1, 0, 1, 6, 76, 12916
Offset: 0

Views

Author

Gus Wiseman, Jun 16 2018

Keywords

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge. A singleton is an edge containing only one vertex.

Examples

			Non-isomorphic representative of the a(3) = 6 set-systems:
{{1,2,3}}
{{1,3},{2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A001206, A051185, A048143, A261006, A058891, A261005, A304998, A305854-A305857, A305935, A306000, A306001, A306008.

Formula

a(n) = A306001(n) - A306001(n-1) for n > 0. - Andrew Howroyd, Aug 12 2019

Extensions

a(5) from Andrew Howroyd, Aug 12 2019

A305935 Number of labeled spanning intersecting set-systems on n vertices with no singletons.

Original entry on oeis.org

1, 0, 1, 12, 809, 1146800, 899927167353, 291136684655893185321964, 14704020783497694096988185391720223222562121969, 12553242487939982849962414795232892198542733492886483991398790450208264017757788101836749760
Offset: 0

Views

Author

Gus Wiseman, Jun 15 2018

Keywords

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge. A singleton is an edge containing only one vertex.

Examples

			The a(3) = 12 spanning intersecting set-systems with no singletons:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,2,3}}
{{1,3},{1,2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
{{1,2},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A001206, A006126, A051185, A048143, A058891, A305001, A305843, A305844, A305854-A305857, A305999, A306000, A306001, A306008.

Formula

a(n) = A305843(n) - n * A003465(n-1).
Inverse binomial transform of A306000. - Andrew Howroyd, Aug 12 2019

Extensions

a(6)-a(8) from Giovanni Resta, Jun 20 2018
a(9) from Andrew Howroyd, Aug 12 2019

A306001 Number of unlabeled intersecting set-systems with no singletons on up to n vertices.

Original entry on oeis.org

1, 1, 2, 8, 84, 13000
Offset: 0

Views

Author

Gus Wiseman, Jun 16 2018

Keywords

Comments

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. A singleton is an edge containing only one vertex.

Examples

			Non-isomorphic representatives of the a(3) = 8 set-systems:
{}
{{1,2}}
{{1,2,3}}
{{1,3},{2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}

Crossrefs

Cf. A001206, A051185, A048143, A261006, A058891, A261005, A304998, A305854-A305857, A305935, A305999, A306000.

Formula

a(n) = A305856(n) - A000612(n). - Andrew Howroyd, Aug 12 2019

Extensions

a(5) from Andrew Howroyd, Aug 12 2019
Showing 1-3 of 3 results.

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