

A001833


Number of labeled graded partially ordered sets with n elements.
(Formerly M3067 N1243)


6



1, 1, 3, 19, 219, 3991, 106623, 3964339, 199515459, 13399883551, 1197639892983, 143076298623259, 23053861370437659, 5062745845287855271, 1530139311543346178223, 641441466132460086890179, 375107113287994040621904819, 307244526491924695346004951151, 353511145615118063468292270299943
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OFFSET

0,3


COMMENTS

Here "graded" means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1. Note that this notion of grading is weaker than in sequence A006860, which counts posets in which all maximal chains have the same length.


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..18.
David A. Klarner, The number of graded partially ordered sets, Journal of Combinatorial Theory, vol.6, no.1, pp.1219, (January1969).
D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 1219. [Annotated scanned copy]
Index entries for sequences related to posets


EXAMPLE

The poset on {a, b, c, d, e} defined by the relations a < b < c and d < e is counted by this sequence. (For example, one associated rank function is rk(a) = rk(d) = 0, rk(b) = rk(e) = 1 and rk(c) = 2.) However, the poset defined by the relations a < b < c and a < d < e < c is not graded and so not counted by this sequence.


CROSSREFS

Graded posets with no chain of length 3 are counted by A001831.
Cf. A006860.
Sequence in context: A135749 A005647 A158876 * A001035 A267634 A277407
Adjacent sequences: A001830 A001831 A001832 * A001834 A001835 A001836


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Corrected and edited by Joel B. Lewis, Mar 28 2011
a(7)a(15) from Daniele P. Morelli, Aug 25 2013
a(16)a(18) from Sean A. Irvine, Sep 25 2015


STATUS

approved



