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

0,27

Links

Table of n, a(n) for n=0..85.

Example

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

Crossrefs

Triangle sums are A007718.

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

Sequence in context: A127309 A097853 A160266 * A023504 A157905 A356718

Adjacent sequences: A322131 A322132 A322133 * A322135 A322136 A322137

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 27 2018

Status

approved