A165452 Number of connected graphs of odd girth at least 7 with n vertices.

1, 1, 1, 3, 5, 17, 45, 184, 748, 4143, 26532, 221032, 2326853, 32202266, 589436301, 14459238676, 477812658943

Offset

1,4

Comments

The odd girth of a graph is the length of a shortest cycle of odd length. Thus, these are the connected graphs that do not have a triangle or C_5 as induced subgraph. - Falk Hüffner, Jan 15 2016

The bipartite graphs (which have no odd cycles) are included.

Links

Table of n, a(n) for n=1..17.

F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version ece94ef.

Crossrefs

Cf. A005142, A024607.

Inverse EULER transform of A345247.

Sequence in context: A236458 A131342 A005142 * A106063 A215106 A368651

Adjacent sequences: A165449 A165450 A165451 * A165453 A165454 A165455

Keyword

nonn

Author

Friedrich Regen (friedrich.regen(AT)tu-ilmenau.de), Sep 20 2009

Extensions

a(15) and a(16) added using tinygraph by Falk Hüffner, Jan 15 2016

a(17) added by Brendan McKay, Jun 12 2021

Status

approved