

A327438


Irregular triangle read by rows with trailing zeros removed where T(n,k) is the number of unlabeled antichains of nonempty subsets of {1..n} with spanning edgeconnectivity k.


2



1, 1, 1, 3, 1, 6, 2, 1, 15, 7, 5, 2, 52, 53, 62, 31, 9, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

An antichain is a set of sets, none of which is a subset of any other.
The spanning edgeconnectivity of a setsystem is the minimum number of edges that must be removed (without removing incident vertices) to obtain a setsystem that is disconnected or covers fewer vertices.


LINKS

Table of n, a(n) for n=0..18.


EXAMPLE

Triangle begins:
1
1 1
3 1
6 2 1
15 7 5 2
52 53 62 31 9 1 1
The antichains counted in row n = 4 are the following:
0 {1234} {12}{134}{234} {123}{124}{134}{234}
{1} {12}{134} {123}{124}{134} {12}{13}{14}{23}{24}{34}
{12} {123}{124} {12}{13}{24}{34}
{123} {12}{13}{14} {12}{13}{14}{234}
{1}{2} {12}{13}{24} {12}{13}{14}{23}{24}
{1}{23} {12}{13}{234}
{12}{13} {12}{13}{14}{23}
{1}{234}
{12}{34}
{1}{2}{3}
{1}{2}{34}
{2}{13}{14}
{12}{13}{23}
{1}{2}{3}{4}
{4}{12}{13}{23}


CROSSREFS

Row sums are A306505.
Column k = 0 is A327437.
The labeled version is A327352.
Cf. A014466, A052446, A327062, A327071, A327103, A327111, A327144, A327352, A327353.
Sequence in context: A055151 A181187 A104573 * A010467 A335320 A182182
Adjacent sequences: A327435 A327436 A327437 * A327439 A327440 A327441


KEYWORD

nonn,tabf,more


AUTHOR

Gus Wiseman, Sep 11 2019


STATUS

approved



