A185143 Number of not necessarily connected 4-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 1, 1, 2, 5, 16, 58, 264, 1535, 10755, 87973, 803973, 8020967, 86029760, 983431053, 11913921910, 152352965278, 2050065073002, 28951233955602, 428086557232387

Offset: 0

Author

Jason Kimberley, Mar 12 2012

Keywords

• nonn
• hard
• more

Links

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

Crossrefs

4-regular simple graphs with girth exactly 3: A184943 (connected), A185043 (disconnected), this sequence (not necessarily connected).

Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), this sequence (k=4), A185153 (k=5), A185163 (k=6).

Not necessarily connected 4-regular simple graphs with girth exactly g: A185140 (triangle); fixed g: this sequence (g=3), A185144 (g=4).

Formula

a(n) = A033301(n) - A185344(n).

a(n) = A184943(n) + A185043(n).

Extensions

a(22) corrected and a(23) appended, due to the correction and extension of A033301 by Andrew Howroyd, from Jason Kimberley, Mar 14 2020