A022017 Number of connected partially ordered sets with n "lines": pairs (a,b) where a < b and there is no c with a < c < b. The lines form the minimal basis for the partial ordering.

1, 3, 8, 29, 103, 442, 1953, 9502, 48533, 262634, 1485764, 8777397, 53869119

Offset

1,2

Comments

The points are unlabeled.

References

See A000112 for references and links about partially ordered sets.

Links

Table of n, a(n) for n=1..13.

N. J. A. Sloane, Illustration of initial terms of A022016 and A022017.

Rico Zöllner and Konrad Handrich, On the Number of Posets, arXiv:2512.08686 [math.CO], 2025. See p. 2.

Index entries for sequences related to posets

Example

See Sloane's link.

Crossrefs

Cf. A000112, A000608, A022016. Column sums of A342590.

Sequence in context: A148872 A148873 A148874 * A148875 A338306 A148876

Adjacent sequences: A022014 A022015 A022016 * A022018 A022019 A022020

Keyword

nonn,hard,more

Author

Franklin T. Adams-Watters, Mar 30 2002

Extensions

a(6)-a(9) from A342590. - R. J. Mathar, Mar 21 2021

a(10)-a(13) from Rico Zöllner and Konrad Handrich, Nov 19 2024

Status

approved