A297877 Triangle T(n,k) read by rows, giving number of bipartite graphs with n nodes (n >= 0) and k edges (0 <= k <= floor(n/2*n/2)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 4, 1, 1, 1, 1, 2, 4, 7, 8, 6, 3, 2, 1, 1, 1, 2, 4, 8, 13, 19, 14, 13, 7, 4, 1, 1, 1, 1, 2, 4, 9, 16, 32, 45, 52, 48, 40, 24, 16, 7, 3, 2, 1, 1, 1, 2, 4, 9, 17, 38, 70, 120, 150, 179, 164, 143, 94, 63, 32, 19, 7, 4, 1, 1, 1, 1, 2, 4, 9, 18, 41, 85, 181, 324, 500, 659

Offset

0,10

Comments

The sum of the m-th row is the (m-1)-st member of A033995, number of bipartite graphs with n nodes.

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, New York / London, 1973.

Links

Table of n, a(n) for n=0..91.

P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49-57.

Juergen Will, Rows 0 to 10 of triangle.

Example

Triangle begins:
0:  1;
1:  1;
2:  1,  1;
3:  1,  1,  1;
4:  1,  1,  2,  2,  1;
5:  1,  1,  2,  3,  4,  1,  1;
6:  1,  1,  2,  4,  7,  8,  6,  3,  2,  1;
7:  1,  1,  2,  4,  8, 13, 19, 14, 13,  7,  4,  1,  1;

Crossrefs

Cf. A033995 (row sums).

Sequence in context: A071127 A029381 A343558 * A027926 A114730 A031282

Adjacent sequences: A297874 A297875 A297876 * A297878 A297879 A297880

Keyword

nonn,tabf

Author

Juergen Will, Jan 07 2018

Status

approved