A356111 The number of 1+1+1-free ordered posets of [n].

1, 1, 2, 6, 23, 102, 497, 2586, 14127, 80146, 468688, 2810163, 17206549, 107261051, 679096359, 4358360362, 28309516828, 185862601727, 1232042778231, 8238155634738, 55521191613041, 376888928783870, 2575334987109807, 17704834935517727, 122401523831513816

Offset

0,3

Comments

A partial order R on [n] is ordered if xRy implies x < y; i.e., the natural order (<) is a linear extension of R. 1+1+1-free posets are those with width (longest antichain) at most 2.

Links

Table of n, a(n) for n=0..24.

Formula

Conjectured g.f.: 2 - 2*x/(B(x)-1+x), where B(x) is the o.g.f. for A001181. - Michael D. Weiner, Oct 04 2024

Example

The six 1+1+1-free ordered posets of [3] are those with covering relations {(1,2)}, {(1,3)}, {(2,3)}, {(1,2), (1,3)}, {(1,2), (2,3)} and {(1,3), (2,3)}.

Crossrefs

See A006455 for the number of all ordered posets on [n], and A135922 for the number of ordered posets on [n] with height at most two.

Cf. A001181.

Sequence in context: A098746 A245389 A088929 * A374550 A279573 A174193

Adjacent sequences: A356108 A356109 A356110 * A356112 A356113 A356114

Keyword

nonn

Author

David Bevan, Jul 27 2022

Status

approved