A106498 Triangle read by rows: T(n,k) = number of unlabeled bicolored graphs with isolated nodes allowed having 2n nodes and k edges, with n nodes of each color. Here n >= 0, 0 <= k <= n^2.
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 4, 5, 5, 4, 2, 1, 1, 1, 1, 2, 4, 10, 13, 23, 26, 32, 26, 23, 13, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 20, 39, 72, 128, 198, 280, 353, 399, 399, 353, 280, 198, 128, 72, 39, 20, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 20, 50, 99, 227, 458, 934, 1711
Offset: 0
Examples
Triangles A106498 and A123547 begin: n = 0 k = 0 : 1, 1 Total = 1, 1 n = 1 k = 0 : 1, 0 k = 1 : 1, 1 Total = 2, 1 n = 2 k = 0 : 1, 0 k = 1 : 1, 0 k = 2 : 2, 1 k = 3 : 1, 1 k = 4 : 1, 1 Totals = 6, 3 n = 3 k = 0 : 1, 0 k = 1 : 1, 0 k = 2 : 2, 0 k = 3 : 4, 1 k = 4 : 5, 2 k = 5 : 5, 4 k = 6 : 4, 3 k = 7 : 2, 2 k = 8 : 1, 1 k = 9 : 1, 1 Totals = 26, 14
References
- R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
Links
- R. W. Robinson, Rows 0 through 7, flattened
- F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning, B 5 (1978), 31-43.
- F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning B: Urban Analytics and City Science, 5 (1978), 31-43. [Annotated scanned copy]
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