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A122084
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Triangle read by rows: T(n,k) = number of unlabeled rooted bicolored trees with n nodes (n >= 1) in which k (1 <= k <= n-1, except k=1 if n=1) nodes have even distance from the root and n-k nodes have odd distance from the root.
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1
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1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 5, 1, 1, 5, 16, 18, 7, 1, 1, 6, 25, 44, 30, 8, 1, 1, 7, 36, 88, 98, 45, 10, 1, 1, 8, 49, 155, 249, 181, 64, 11, 1, 1, 9, 64, 250, 535, 576, 308, 85, 13, 1, 1, 10, 81, 377, 1021, 1506, 1166, 479, 110, 14, 1, 1, 11, 100, 542, 1786
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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REFERENCES
| R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
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LINKS
| R. W. Robinson, Rows 1 through 30, flattened
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EXAMPLE
| K M N gives the number N of unlabeled rooted bicolored trees in which K nodes have even distance from the root and M nodes have odd distance from the root.
1 0 1
Total( 1) = 1
1 1 1
Total( 2) = 1
1 2 1
2 1 1
Total( 3) = 2
1 3 1
2 2 2
3 1 1
Total( 4) = 4
1 4 1
2 3 3
3 2 4
4 1 1
Total( 5) = 9
1 5 1
2 4 4
3 3 9
4 2 5
5 1 1
Total( 6) = 20
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CROSSREFS
| Row sums give A000081.
Sequence in context: A096465 A124460 A144042 * A104559 A080853 A071922
Adjacent sequences: A122081 A122082 A122083 * A122085 A122086 A122087
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KEYWORD
| nonn,tabf
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 19 2006
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