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A028657
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Triangle T(n,k) of number of n node graphs with k nodes in distinguished bipartite block, k=0..n.
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4
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 22, 36, 22, 6, 1, 1, 7, 34, 87, 87, 34, 7, 1, 1, 8, 50, 190, 317, 190, 50, 8, 1, 1, 9, 70, 386, 1053, 1053, 386, 70, 9, 1, 1, 10, 95, 734, 3250, 5624, 3250, 734, 95, 10, 1, 1, 11, 125, 1324, 9343, 28576
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Also, row n gives the number of unlabeled bicolored graphs having k nodes of one color and n-k nodes of the other color; the color classes are not interchangeable.
Also the number of principal transversal matroids (a.k.a. fundamental transversal matroids) of size n and rank k (originally enumerated by Brylawski). - Gordon Royle (gordon(AT)maths.uwa.edu.au), Oct 30 2007
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REFERENCES
| R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
Brylawski, Thomas H., An affine representation for transversal geometries. Studies in Appl. Math. 54 (1975), no. 2, 143--160.
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LINKS
| R. W. Robinson, The first 20 rows, flattened
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EXAMPLE
| [1], [1,1], [1,2,1], [1,3,3,1], [1,4,7,4,1], [1,5,13,13,5,1], [1,6,22,36,22,6,1], ...; there are 36 graphs on 6 nodes with a distinguished bipartite block with 3 nodes.
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CROSSREFS
| Row sums give A049312.
Cf. A055080, A049312.
Sequence in context: A094526 A088699 A101515 * A053534 A104881 A171699
Adjacent sequences: A028654 A028655 A028656 * A028658 A028659 A028660
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KEYWORD
| nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 16 2000
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