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A301560
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Matching number of the n-odd graph.
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2
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0, 1, 5, 17, 63, 231, 858, 3217, 12155, 46189, 176358, 676039, 2600150, 10029150, 38779380, 150270097, 583401555, 2268783825, 8836315950, 34461632205, 134564468610, 526024740930, 2058357681900, 8061900920775, 31602651609438, 123979633237026, 486734856412028
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OFFSET
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1,3
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COMMENTS
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The n-odd graph is known to be Hamiltonian for 4 <= n <= 14. Hamiltonian graphs always have a matching with at most one unmatched vertex. - Andrew Howroyd, Mar 23 2018 [Now known for all n >= 4. - Pontus von Brömssen, May 01 2020]
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LINKS
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Eric Weisstein's World of Mathematics, Odd Graph
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FORMULA
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a(n) = floor(binomial(2*n - 1, n - 1)/2).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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