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 A005816 Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed. (Formerly M3006) 3
 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, A033301. Sequence in context: A267018 A262911 A163949 * A179470 A270524 A179471 Adjacent sequences:  A005813 A005814 A005815 * A005817 A005818 A005819 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 January 21 05:13 EST 2022. Contains 350473 sequences. (Running on oeis4.)