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A005816
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Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed.
(Formerly M3006)
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2
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1, 1, 3, 15, 138, 2021, 43581, 1295493, 50752145, 2533755933, 157055247261, 11836611005031, 1066129321651668, 113117849882149725, 13965580274228976213, 1985189312618723797371, 321932406123733248625851, 59079829666712346141491403, 12182062872168618012045410805
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Each loop contributes 2 to the valency of its node.
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REFERENCES
| Goulden, I. P.; Jackson, D. M.; Reilly, J. W.; The Hammond series of a symmetric function and its application to $P$-recursiveness. SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 179-193.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| J. S. Kimberley, Table of n, a(n) for n=0..25 [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Feb 17 2010]
R. C. Read, The enumeration of locally restricted graphs (I), J. London Math. Soc. 34 (1959) 417-436.
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FORMULA
| N\{E_n[S_4] * S_{2n}[S_2]\}.
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CROSSREFS
| Cf. A005815.
Cf. A129429, A033301 [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Feb 17 2010]
Sequence in context: A113723 A113379 A163949 * A179470 A179471 A203417
Adjacent sequences: A005813 A005814 A005815 * A005817 A005818 A005819
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Definition corrected by appending "where multiple edges and loops are allowed", reference to Read 1959, formula from Read 1959 (5.11), and new terms a(16), a(17), a(18) contributed by Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Jan 22 2010
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