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A095268
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Number of distinct degree sequences among all n-vertex graphs with no isolated vertices.
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2
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1, 2, 7, 20, 71, 240, 871, 3148, 11655, 43332, 162769, 614198, 2330537, 8875768, 33924859, 130038230, 499753855, 1924912894, 7429160296, 28723877732, 111236423288, 431403470222
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| A002494 is the number of graphs on n nodes with no isolated points and A095268 is the number of these graphs having distinct degree sequences.
Comment from Gordon Royle, Aug 29 2006: Is it true that a(n+1)/a(n) tends to 4? Is there are a heuristic argument why this might be true?
Comment from Paul Hanna, Aug 18, 2006: Now that more terms have been computed, we can see that this is not the self-convolution of any integer sequence.
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LINKS
| Frank Ruskey, Title?
Eric Weisstein's World of Mathematics, Degree sequence
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EXAMPLE
| a(4) = 7 because a 4-vertex graph with no isolated vertices can have degree sequence 1111, 2211, 2222, 3111, 3221, 3322 or 3333.
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CROSSREFS
| Cf. A000569, A002494, A004250; A007721 (analogue for connected graphs).
Sequence in context: A000150 A115117 A029890 * A118397 A171191 A189771
Adjacent sequences: A095265 A095266 A095267 * A095269 A095270 A095271
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KEYWORD
| nonn,more
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), May 31, 2004
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 26 2006
More terms from Gordon Royle (gordon(AT)maths.uwa.edu.au), Aug 21 2006
a(21) and a(22) from Frank Ruskey, Aug 29 2006
a(23) from Frank Ruskey, Aug 31 2006
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