A185335 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 5.

1, 0, 0, 0, 0, 1, 2, 9, 49, 455, 5784, 90940, 1620491, 31478651, 656784488, 14621878339, 345975756388

Offset: 0

Author

Jason Kimberley, Jan 28 2011

Keywords

• nonn
• more
• hard

Links

• Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Crossrefs

3-regular simple graphs with girth at least 5: A014372 (connected), A185235 (disconnected), this sequence (not necessarily connected).

Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), this sequence (g=5), A185336 (g=6).

Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), A185305 (triangle); specified degree k: A185325 (k=2), this sequence (k=3).

Programs

Mathematica

A014372 = Cases[Import["https://oeis.org/A014372/b014372.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014372] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Formula

This sequence is the Euler transformation of A014372.