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.

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

1,8

Links

Table of n, a(n) for n=1..45.

Wikipedia, Bipartite dimension

Formula

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

Example

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

Crossrefs

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

Sequence in context: A253179 A300723 A263788 * A292144 A300324 A298368

Adjacent sequences: A355332 A355333 A355334 * A355336 A355337 A355338

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Jun 29 2022

Status

approved