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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. 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 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  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 A182182 A158823

Adjacent sequences:  A327435 A327436 A327437 * A327440 A327441 A327442

KEYWORD

nonn,tabf,more

AUTHOR

Gus Wiseman, Sep 11 2019

STATUS

approved

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Last modified October 21 16:50 EDT 2019. Contains 328302 sequences. (Running on oeis4.)