

A222866


Triangle T(n,k) of weakly graded (3+1)free partially ordered sets (posets) on n labeled vertices with height k.


2



1, 1, 2, 1, 12, 6, 1, 86, 84, 24, 1, 840, 1110, 480, 120, 1, 11642, 16620, 9120, 3240, 720, 1, 227892, 300846, 185640, 82320, 25200, 5040, 1, 6285806, 6810804, 4299624, 2142000, 816480, 221760, 40320, 1, 243593040, 199239270, 117205200, 60890760, 26157600
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OFFSET

1,3


COMMENTS

Here "weakly graded" means that there is a rank function rk from the vertices to the integers such that whenever x covers y we have rk(x) = rk(y) + 1. Alternate terminology includes "graded" and "ranked." A poset is said to be (3+1)free if it does not contain four elements a, b, c, d such that a < b < c and d is incomparable to the other three.


LINKS

Joel B. Lewis, Rows n = 1..20 of triangle, flattened
J. B. Lewis and Y. X. Zhang, Enumeration of Graded (3+1)Avoiding Posets, J. Combin. Theory Ser. A 120 (2013), no. 6, 13051327.


FORMULA

G.F. is given in the LewisZhang paper.


CROSSREFS

For rowsums (weakly graded (3+1)free posets with n labeled vertices, disregarding height), see A222865. For strongly graded (3+1)free posets, see A222863. For all weakly graded posets, see A001833. For all (3+1)free posets, see A079145.
Sequence in context: A048743 A049055 A276998 * A008285 A119274 A066991
Adjacent sequences: A222863 A222864 A222865 * A222867 A222868 A222869


KEYWORD

nonn,tabl


AUTHOR

Joel B. Lewis, Mar 07 2013


STATUS

approved



