A185044 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 15, 35, 247, 1692, 17409, 197924, 2492824, 33117880, 461597957, 6709514218, 101153412903, 1597440868898

Offset: 0

Author

Jason Kimberley, Nov 04 2011

Keywords

• nonn
• hard
• more

Comments

Only one component need have girth exactly four; the other components need only have girth at least four.

First differs from A185244 at n = 38, the smallest n where A185245 is nonzero.

Links

• Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Crossrefs

Disconnected 4-regular simple graphs with girth exactly g: A185043 (g=3), this sequence (g=4).

Disconnected k-regular simple graphs with girth exactly 4: A185034 (k=3), this sequence (k=4).

Formula

a(n) = A185244(n) - A185245(n).

a(n) = A185144(n) - A184944(n).

Extensions

a(31) corrected by the author, propagated from A185244, Jan 05 2013