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Search: id:A122087
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| A122087 |
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Triangle read by rows: T(n,k) = number of unlabeled free bicolored trees with n nodes (n >= 1) and k (1 <= k <= floor(n/2), except k = 0 if n = 1 ) nodes of one color and n-k nodes of the other color (the colors are interchangeable). |
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+0
1
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| 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 3, 7, 1, 3, 10, 9, 1, 4, 14, 28, 1, 4, 19, 45, 37, 1, 5, 24, 73, 132, 1, 5, 30, 105, 242, 168, 1, 6, 37, 152, 412, 693, 1, 6, 44, 204, 660, 1349, 895, 1, 7, 52, 274, 1008, 2472, 3927, 1, 7, 61, 351, 1479, 4219, 8105, 5097, 1, 8
(list; graph; listen)
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OFFSET
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1,7
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REFERENCES
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R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
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LINKS
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R. W. Robinson, Rows 1 through 30, flattened
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EXAMPLE
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K M N gives the number N of unlabeled free bicolored trees with K nodes of one color and M nodes of the other color.
0 1 1
Total( 1) = 1
1 1 1
Total( 2) = 1
1 2 1
Total( 3) = 1
1 3 1
2 2 1
Total( 4) = 2
1 4 1
2 3 2
Total( 5) = 3
1 5 1
2 4 2
3 3 3
Total( 6) = 6
1 6 1
2 5 3
3 4 7
Total( 7) = 11
1 7 1
2 6 3
3 5 10
4 4 9
Total( 8) = 23
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CROSSREFS
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Row sums give A000055.
Sequence in context: A104468 A110062 A144215 this_sequence A139642 A143604 A021475
Adjacent sequences: A122084 A122085 A122086 this_sequence A122088 A122089 A122090
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 19 2006
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