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.
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
KEYWORD
nonn
AUTHOR
David Bevan, Jul 27 2022
STATUS
approved