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Search: id:A122083
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| A122083 |
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Triangle read by rows in which row n gives the number of unlabeled bicolored graphs having k nodes of one color and n-k nodes of the other color, with no isolated nodes; the color classes are not interchangeable. |
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3
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| 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 3, 1, 0, 0, 1, 5, 5, 1, 0, 0, 1, 8, 17, 8, 1, 0, 0, 1, 11, 42, 42, 11, 1, 0, 0, 1, 15, 91, 179, 91, 15, 1, 0, 0, 1, 19, 180, 633, 633, 180, 19, 1, 0, 0, 1, 24, 328, 2001, 3835, 2001, 328, 24, 1, 0, 0, 1, 29, 565, 5745, 20755, 20755
(list; table; graph; listen)
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OFFSET
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0,13
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REFERENCES
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J. G. Lee, Almost Distributive Lattice Varieties, Algebra Universalis, 21 (1985), 280-304.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
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LINKS
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R. W. Robinson, First 20 rows, flattened
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EXAMPLE
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K M N Gives the number N of unlabeled bicolored graphs with no isolated nodes and having K nodes of one color and M nodes of the other color.
0 0 1
Total( 0)= 1
0 1 0
1 0 0
Total( 1)= 0
0 2 0
1 1 1
2 0 0
Total( 2)= 1
0 3 0
1 2 1
2 1 1
3 0 0
Total( 3)= 2
0 4 0
1 3 1
2 2 3
3 1 1
4 0 0
Total( 4)= 5
0 5 0
1 4 1
2 3 5
3 2 5
4 1 1
5 0 0
Total( 5)= 12
0 6 0
1 5 1
2 4 8
3 3 17
4 2 8
5 1 1
6 0 0
Total( 6)= 35
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CROSSREFS
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Row sums give A055192. See A056152 for a version of this triangle with the bounding zeros in each row.
Sequence in context: A094544 A062734 A117389 this_sequence A098158 A110319 A036872
Adjacent sequences: A122080 A122081 A122082 this_sequence A122084 A122085 A122086
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KEYWORD
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nonn,tabl
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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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