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A005816 Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed.
(Formerly M3006)
4
1, 1, 3, 15, 138, 2021, 43581, 1295493, 50752145, 2533755933, 157055247261, 11836611005031, 1066129321651668, 113117849882149725, 13965580274228976213, 1985189312618723797371, 321932406123733248625851, 59079829666712346141491403, 12182062872168618012045410805 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Each loop contributes 2 to the valency of its node.
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).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 0..25 from Jason Kimberley)
R. C. Read, The enumeration of locally restricted graphs (I), J. London Math. Soc. 34 (1959) 417-436.
FORMULA
a(n) = N{E_n[S_4] * S_{2n}[S_2]}.
CROSSREFS
Column k=4 of A333467.
Cf. A005815.
Cf. A129429 (unlabeled), A033301.
Sequence in context: A267018 A262911 A163949 * A179470 A270524 A179471
KEYWORD
nonn
AUTHOR
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, Jan 22 2010
STATUS
approved

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Last modified March 29 09:28 EDT 2024. Contains 371268 sequences. (Running on oeis4.)