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A165655
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Number of disconnected 5-regular (quintic) graphs on 2n vertices.
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12
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0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484760, 2595985770, 2815099031417, 4230059694039460, 8529853839173455678, 22496718465713456081402, 75951258300080722467845995, 322269241532759484921710401976
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OFFSET
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0,8
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LINKS
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Table of n, a(n) for n=0..17.
N. J. A. Sloane, Transforms
Jason Kimberley, Disconnected regular graphs (with girth at least 3)
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g
Eric Weisstein's World of Mathematics, Disconnected Graph
Eric Weisstein's World of Mathematics, Quintic Graph
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FORMULA
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a = A165626 - A006821 = Euler_transformation(A006821) - A006821.
a(n)=A068933(2n,5).
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CROSSREFS
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5-regular simple graphs: A006821 (connected), this sequence (disconnected), A165626 (not necessarily connected).
Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), A033483 (k=4), this sequence (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).
Sequence in context: A187547 A157554 A185053 * A157576 A339599 A105443
Adjacent sequences: A165652 A165653 A165654 * A165656 A165657 A165658
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KEYWORD
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nonn,hard,more
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AUTHOR
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Jason Kimberley, Sep 28 2009
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EXTENSIONS
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Terms a(13)-a(17), due to the extension of A006821 by Andrew Howroyd, from Jason Kimberley, Mar 12 2020
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STATUS
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approved
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