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Search: id:A122085
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| A122085 |
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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 <= n-1, except k=0 or 1 if n=1, k=1 if n=2) nodes of one color and n-k nodes of the other color (the colors are not interchangeable). |
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+0
2
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 7, 7, 3, 1, 1, 3, 10, 14, 10, 3, 1, 1, 4, 14, 28, 28, 14, 4, 1, 1, 4, 19, 45, 65, 45, 19, 4, 1, 1, 5, 24, 73, 132, 132, 73, 24, 5, 1, 1, 5, 30, 105, 242, 316, 242, 105, 30, 5, 1, 1, 6, 37, 152, 412, 693, 693, 412, 152
(list; graph; listen)
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OFFSET
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1,10
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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
1 0 1
Total( 1) = 2
1 1 1
Total( 2) = 1
1 2 1
2 1 1
Total( 3) = 2
1 3 1
2 2 1
3 1 1
Total( 4) = 3
1 4 1
2 3 2
3 2 2
4 1 1
Total( 5) = 6
1 5 1
2 4 2
3 3 4
4 2 2
5 1 1
Total( 6) = 10
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CROSSREFS
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Row sums give A122086.
Sequence in context: A075402 A088855 A034851 this_sequence A066287 A059260 A135229
Adjacent sequences: A122082 A122083 A122084 this_sequence A122086 A122087 A122088
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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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