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

0,3

Links

Table of n, a(n) for n=0..21.

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

Formula

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

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

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).

Sequence in context: A078658 A307719 A351594 * A285120 A282744 A195310

Adjacent sequences: A185311 A185312 A185313 * A185315 A185316 A185317

Keyword

nonn,more,hard

Author

Jason Kimberley, May 23 2012

Status

approved