A334335 Inverse Euler transform of A000568.

1, 0, 1, 2, 8, 43, 398, 6413, 184596, 9540998, 894012628, 153204356304, 48387996396590, 28352880689501075, 30992600581556641380, 63499394791445838416399, 244849247994227524521679624, 1783153933475289754036309451798, 24603857772350530383609071261316942

Offset

1,4

Comments

It appears that a(n) is the number of connected even graphs with n vertices, as defined in the Andersson paper (verified for n <= 10): a graph G is even if, for a given orientation of its edges, all automorphisms of G reverse the orientation of an even number of edges. If this is true, it means that A000568(n) is the number of even graphs (not necessarily connected) with n vertices. [This has been proved by Royle et al. 2023. - Pontus von Brömssen, Apr 06 2022]

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..76

Pontus Andersson (von Brömssen), On the asymptotic distributions of subgraph counts in a random tournament, Random Structures & Algorithms 13 (1998), 249-260.

Gordon F. Royle, Cheryl E. Praeger, S. P. Glasby, Saul D. Freedman, and Alice Devillers, Tournaments and even graphs are equinumerous, Journal of Algebraic Combinatorics 57 (2023), 515-524; arXiv version, arXiv:2204.01947 [math.CO], 2022.

Crossrefs

Cf. A000568.

Sequence in context: A009309 A276497 A324670 * A283416 A075817 A264565

Adjacent sequences: A334332 A334333 A334334 * A334336 A334337 A334338

Keyword

nonn

Author

Pontus von Brömssen, Apr 23 2020

Status

approved