A198313 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 1, 1, 1, 4, 4, 15, 23, 162, 540, 18958, 389417, 50314520, 2942196930, 1698517018988

Offset: 0

Author

Jason Kimberley, May 24 2012

Keywords

• nonn
• more
• hard

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 3: this sequence (any k), A185643 (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6).

Not necessarily connected regular simple graphs girth exactly g: this sequence (g=3), A198314 (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

Formula

a(n) = A186743(n) + A210713(n).

a(n) = A005176(n) - A185314(n).

a(n) is the sum of the n-th row of A185643.