A317533 -id:A317533 - cp's OEIS frontend

A322134 Regular tetrangle where T(n,k,i) is the number of unlabeled connected multiset partitions of weight n with k vertices and i edges.

1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 4, 2, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 2, 7, 6, 2, 2, 6, 4, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 3, 3, 2, 1, 1, 3, 14, 17, 9, 3, 3, 17, 18, 7, 2, 9, 7, 1, 3, 1, 0, 0

Offset: 0

Gus Wiseman, Nov 27 2018

			Tetrangle begins:
  1
.
  0 0
  1
.
  0 0 0
  1 1
  1
.
  0 0 0 0
  1 1 1
  1 1
  1
.
  0 0 0 0 0
  1 2 1 1
  2 4 2
  1 2
  1
.
  0 0 0 0 0 0
  1 2 2 1 1
  2 7 6 2
  2 6 4
  1 2
  1
.
  0  0  0  0  0  0  0
  1  3  3  2  1  1
  3 14 17  9  3
  3 17 18  7
  2  9  7
  1  3
  1
.
  0  0  0  0  0  0  0  0
  1  3  4  3  2  1  1
  3 20 33 24 11  3
  4 33 59 35 10
  3 24 35 14
  2 11 10
  1  3
  1

Triangle sums are A007718.

Cf. A007716, A054923, A191646, A191970, A275421, A286520, A317533, A317672, A321155, A321254, A322114.

A330464 Number of non-isomorphic weight-n sets of set-systems with distinct multiset unions.

Original entry on oeis.org

1, 1, 3, 9, 32, 111, 463, 1942

Offset: 0

Gus Wiseman, Dec 26 2019

A set-system is a finite set of finite nonempty sets of positive integers.

As an alternative description, a(n) is the number of non-isomorphic sets of sets of sets with n leaves where the inner sets of sets all have different multiset unions.

			Non-isomorphic representatives of the a(1) = 1 through a(3) = 9 sets:
  {}  {{{1}}}  {{{1,2}}}      {{{1,2,3}}}
               {{{1},{2}}}    {{{1},{1,2}}}
               {{{1}},{{2}}}  {{{1},{2,3}}}
                              {{{1}},{{1,2}}}
                              {{{1}},{{2,3}}}
                              {{{1},{2},{3}}}
                              {{{1}},{{1},{2}}}
                              {{{1}},{{2},{3}}}
                              {{{1}},{{2}},{{3}}}

Non-isomorphic sets of sets are A283877.
Non-isomorphic sets of sets of sets are A323790.
Non-isomorphic set partitions of set-systems are A323795.
Cf. A089259, A141268, A271619, A279375, A279785, A306186, A316980, A317533, A318564, A318565, A318566, A330459, A330472.

cp's OEIS Frontend

A322134 Regular tetrangle where T(n,k,i) is the number of unlabeled connected multiset partitions of weight n with k vertices and i edges.

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