A307317 Number of unlabeled connected leafless loopless multigraphs with n edges.

1, 0, 1, 2, 4, 9, 26, 68, 217, 718, 2553, 9574, 38005, 157306, 679682, 3047699, 14150278, 67844305, 335262807, 1704500229, 8902528600, 47704608478, 261960998230, 1472618327415, 8466681788462, 49743177379613, 298407523833717, 1826531247381194, 11399711132242500, 72500116125222893, 469578870456459042

Offset

0,4

Comments

Connected multigraphs with no loops and no vertices of degree 1.

The initial terms were computed with Nauty.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

P. T. Komiske, E. M. Metodiev, and J. Thaler, Cutting Multiparticle Correlators Down to Size, arXiv:1911.04491 [hep-ph], 2019-2020.

Brendan McKay and Adolfo Piperno, nauty and Traces.

Formula

Inverse Euler transform of A307316.

Example

For n=3 the multigraphs (as sets of edges) are {(0,1),(0,1),(0,1)} and {(0,1),(0,2),(1,2)}.

Crossrefs

Cf. A076864, A307316 (not necessarily connected), A342556 (simple graphs).

Sequence in context: A124835 A125799 A220880 * A188669 A243568 A087378

Adjacent sequences: A307314 A307315 A307316 * A307318 A307319 A307320

Keyword

nonn

Author

Eric M. Metodiev, Apr 02 2019

Extensions

a(0)=1 prepended and a(17) onwards from Andrew Howroyd, Feb 01 2024

Status

approved