The odd girth of a graph is the length of a shortest cycle of odd length. Thus, these are the graphs (not necessarily connected) that do not have a triangle or C_5 as a subgraph. The bipartite graphs (which have no odd cycles) are included.
Table of n, a(n) for n=1..17.
EULER transform of A165452.
Sequence in context: A006840 A123408 A033995 * A013917 A293994 A196419
Adjacent sequences: A345244 A345245 A345246 * A345248 A345249 A345250
Brendan McKay, Jun 12 2021