A185314 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 4.

1, 1, 2, 1, 3, 2, 4, 2, 7, 3, 14, 6, 44, 37, 350, 1616, 18042, 193919, 2867779, 32674078, 1581632332, 6705889886

Offset: 0

Author

Jason Kimberley, May 23 2012

Keywords

• nonn
• more
• hard

Links

• Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 4
• Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Crossrefs

Regular graphs, of any degree, with girth at least 4: A186724 (connected), A185214 (disconnected), this sequence (not-necessarily connected).

Not necessarily connected k-regular simple graphs with girth at least 4: this sequence (any k), A185304 (triangle); specified degree k: A008484 (k=2), A185334 (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), this sequence (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), A185318 (g=8), A185319 (g=9).

Formula

a(n) = A186724(n) + A185214(n).

a(n) is the sum of the n-th row of A185304.