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Search: id:A127909
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| A127909 |
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Number of different digraphs on n unlabeled nodes which are not graphs. |
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+0
4
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| 0, 0, 1, 12, 207, 9574, 1540788, 882032396, 1793359180502, 13027956824124884, 341260431952960575184, 32522909385055885092199576, 11366745430825400574268802831632
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A digraph is (isomorphic to) a graph if every pair of points a, b joined by a directed edge (a,b) also has the reverse directed edge (b,a). A digraph which is not a graph is a digraph with at least one pair of points which have only one directed edge connecting them.
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FORMULA
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a(n) = A000273(n) - A000088(n).
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EXAMPLE
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a(2) = 1 because with two points a and b, either there are no edges connecting them, or there is one directed edge between them, or there is a bidirectional pair of edges between them; only the case with one directed edge is the unique 2-point digraph which is not a graph.
a(3) = 12 because A000273(3) = number of directed graphs (or digraphs) with 3 nodes = 16; A000088(3) = number of graphs on 3 unlabeled nodes = 4; 16-4 = 12.
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CROSSREFS
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Cf. A000088, A000273, A127910-A127915.
Sequence in context: A097193 A051688 A151590 this_sequence A129466 A027399 A027487
Adjacent sequences: A127906 A127907 A127908 this_sequence A127910 A127911 A127912
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 06 2007
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