

A326573


Number of connected antichains of subsets of {1..n}, all having different sums.


5




OFFSET

0,4


COMMENTS

An antichain is a finite set of finite sets, none of which is a subset of any other. It is covering if its union is {1..n}. The edgesums are the sums of vertices in each edge, so for example the edge sums of {{1,3},{2,5},{3,4,5}} are {4,7,12}.


LINKS

Table of n, a(n) for n=0..6.


EXAMPLE

The a(3) = 5 antichains:
{{1,2,3}}
{{1,3},{2,3}}
{{1,2},{2,3}}
{{1,2},{1,3}}
{{1,2},{1,3},{2,3}}
The a(4) = 59 antichains:
{1234} {12}{134} {12}{13}{14} {12}{13}{14}{24} {12}{13}{14}{24}{34}
{12}{234} {12}{13}{24} {12}{13}{14}{34} {12}{13}{23}{24}{34}
{13}{124} {12}{13}{34} {12}{13}{23}{24}
{13}{234} {12}{14}{34} {12}{13}{23}{34}
{14}{123} {12}{23}{24} {12}{13}{24}{34}
{14}{234} {12}{23}{34} {12}{14}{24}{34}
{23}{124} {12}{24}{34} {12}{23}{24}{34}
{23}{134} {13}{14}{24} {13}{14}{24}{34}
{24}{134} {13}{23}{24} {13}{23}{24}{34}
{34}{123} {13}{23}{34} {12}{13}{14}{234}
{123}{124} {13}{24}{34} {12}{23}{24}{134}
{123}{134} {14}{24}{34} {123}{124}{134}{234}
{123}{234} {12}{13}{234}
{124}{134} {12}{14}{234}
{124}{234} {12}{23}{134}
{134}{234} {12}{24}{134}
{13}{14}{234}
{13}{23}{124}
{14}{34}{123}
{23}{24}{134}
{12}{134}{234}
{13}{124}{234}
{14}{123}{234}
{23}{124}{134}
{123}{124}{134}
{123}{124}{234}
{123}{134}{234}
{124}{134}{234}


CROSSREFS

Antichain covers are A006126.
Connected antichains are A048143.
Set partitions with different blocksums are A275780.
MMnumbers of multiset partitions with different partsums are A326535.
Antichain covers with equal edgesums are A326566.
The nonconnected case is A326572.
Cf. A000372, A293510, A307249, A321469, A323818, A326519, A326565, A326569, A326570, A326571.
Sequence in context: A249519 A001059 A290702 * A324240 A120608 A143766
Adjacent sequences: A326570 A326571 A326572 * A326574 A326575 A326576


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Jul 18 2019


STATUS

approved



