A005816 Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed. (Formerly M3006)

1, 1, 3, 15, 138, 2021, 43581, 1295493, 50752145, 2533755933, 157055247261, 11836611005031, 1066129321651668, 113117849882149725, 13965580274228976213, 1985189312618723797371, 321932406123733248625851, 59079829666712346141491403, 12182062872168618012045410805

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

Adjacent sequences: A005813 A005814 A005815 * A005817 A005818 A005819

Keyword

nonn

Author

Simon Plouffe

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