A198314 Number of, not necessarily connected, regular simple graphs on n vertices with girth exactly 4.

0, 0, 0, 0, 1, 0, 1, 0, 4, 1, 8, 3, 37, 33, 335, 1610, 17985, 193911, 2867313, 32674066, 1581626531, 6705889862

Offset: 0

Author

Jason Kimberley, Dec 12 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 4: this sequence (any k), A185644 (triangle); fixed k: A026797 (k=2), A185134 (k=3), A185144 (k=4).

Not necessarily connected regular simple graphs girth exactly g: A198313 (g=3), this sequence (g=4), A198315 (g=5), A198316 (g=6), A198317 (g=7), A198318 (g=8).

Formula

a(n) = A186744(n) + A210714(n).

a(n) = A185314(n) - A185315(n).

Extensions

a(10) corrected from 9 to 8 by Jason Kimberley, Feb 22 2013