A185134 Number of, not necessarily connected, 3-regular simple graphs on 2n vertices with girth exactly 4.

0, 0, 0, 1, 2, 5, 21, 103, 752, 7385, 91939, 1345933, 22170664, 401399440, 7887389438, 166897766824, 3781593764772

Offset: 0

Author

Jason Kimberley, Mar 21 2012

Keywords

• nonn
• hard
• more

Links

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

Crossrefs

Not necessarily connected k-regular simple graphs girth exactly 4: A198314 (any k), A185644 (triangle); fixed k: A026797 (k=2), this sequence (k=3), A185144 (k=4).

Not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g: A185130 (triangle); fixed g: A185133 (g=3), this sequence (g=4), A185135 (g=5), A185136 (g=6).

Formula

a(n) = A185334(n) - A185335(n).

a(n) = A006924(n) + A185034(n).