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
Examples
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;
References
- F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, New York / London, 1973.
Links
- P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49-57.
- Juergen Will, Rows 0 to 10 of triangle.
Crossrefs
Cf. A033995 (row sums).
Comments