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A333330
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Array read by antidiagonals: T(n,k) is the number of k-regular loopless multigraphs on n unlabeled nodes, n >= 0, k >= 0.
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13
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1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 3, 2, 1, 1, 1, 0, 1, 0, 4, 0, 4, 0, 1, 1, 0, 1, 1, 5, 7, 9, 4, 1, 1, 1, 0, 1, 0, 7, 0, 24, 0, 7, 0, 1, 1, 0, 1, 1, 8, 16, 54, 60, 32, 8, 1, 1, 1, 0, 1, 0, 10, 0, 128, 0, 240, 0, 12, 0, 1, 1, 0, 1, 1, 12, 37, 271, 955, 1753, 930, 135, 14, 1, 1
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OFFSET
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0,26
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COMMENTS
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Terms may be computed without generating each graph by enumerating the number of graphs by degree sequence. A PARI program showing this technique for graphs with labeled vertices is given in A333351. Burnside's lemma can be used to extend this method to the unlabeled case.
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LINKS
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EXAMPLE
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Array begins:
=================================================
n\k | 0 1 2 3 4 5 6 7 8
----+--------------------------------------------
0 | 1 1 1 1 1 1 1 1 1 ...
1 | 1 0 0 0 0 0 0 0 0 ...
2 | 1 1 1 1 1 1 1 1 1 ...
3 | 1 0 1 0 1 0 1 0 1 ...
4 | 1 1 2 3 4 5 7 8 10 ...
5 | 1 0 2 0 7 0 16 0 37 ...
6 | 1 1 4 9 24 54 128 271 582 ...
7 | 1 0 4 0 60 0 955 0 12511 ...
8 | 1 1 7 32 240 1753 13467 90913 543779 ...
9 | 1 0 8 0 930 0 253373 0 35255015 ...
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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