A327438 - OEIS

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 edge-connectivity k.

1, 1, 1, 3, 1, 6, 2, 1, 15, 7, 5, 2, 52, 53, 62, 31, 9, 1, 1

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OFFSET

0,4

COMMENTS

An antichain is a set of sets, none of which is a subset of any other.

The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.

LINKS

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

EXAMPLE

Triangle begins:

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