A355336 -id:A355336 - cp's OEIS frontend

A355334 Triangle read by rows: T(n,k) is the number of unlabeled graphs with n nodes and bipartite dimension (or biclique covering number) k, 0 <= k < n.

1, 1, 1, 1, 2, 1, 1, 4, 6, 0, 1, 6, 20, 7, 0, 1, 9, 61, 80, 5, 0, 1, 12, 159, 650, 221, 1, 0, 1, 16, 381, 4710, 6866, 372, 0, 0, 1, 20, 832, 29921, 183618, 59950, 326, 0, 0

Offset: 1

Pontus von Brömssen, Jun 29 2022

			Triangle begins:
  n\k | 0  1   2     3      4     5   6  7  8
  ----+--------------------------------------
   1  | 1
   2  | 1  1
   3  | 1  2   1
   4  | 1  4   6     0
   5  | 1  6  20     7      0
   6  | 1  9  61    80      5     0
   7  | 1 12 159   650    221     1   0
   8  | 1 16 381  4710   6866   372   0  0
   9  | 1 20 832 29921 183618 59950 326  0  0

Wikipedia, Bipartite dimension

Cf. A000088 (row sums), A355333, A355335, A355336.

Columns: A000012 (k=0), A002620 (k=1).

A355335 Triangle read by rows: T(n,k) is the number of unlabeled connected graphs with n nodes and bipartite dimension (or biclique covering number) k, 0 <= k < n.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 2, 4, 0, 0, 2, 13, 6, 0, 0, 3, 38, 67, 4, 0, 0, 3, 94, 550, 205, 1, 0, 0, 4, 214, 3996, 6543, 360, 0, 0, 0, 4, 441, 25037, 176012, 59266, 320, 0, 0

Offset: 1

Pontus von Brömssen, Jun 29 2022

			Triangle begins:
  n\k | 0  1   2     3      4     5   6  7  8
  ----+--------------------------------------
   1  | 1
   2  | 0  1
   3  | 0  1   1
   4  | 0  2   4     0
   5  | 0  2  13     6      0
   6  | 0  3  38    67      4     0
   7  | 0  3  94   550    205     1   0
   8  | 0  4 214  3996   6543   360   0  0
   9  | 0  4 441 25037 176012 59266 320  0  0

Wikipedia, Bipartite dimension

Cf. A001349 (row sums), A004526 (column k=1), A355334, A355336.

T(n,1) = floor(n/2) = A004526(n).

cp's OEIS Frontend

A355334 Triangle read by rows: T(n,k) is the number of unlabeled graphs with n nodes and bipartite dimension (or biclique covering number) k, 0 <= k < n.

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