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

0,9

Links

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

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

Formula

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

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

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).

Sequence in context: A201661 A376815 A263498 * A105534 A021243 A340531

Adjacent sequences: A198311 A198312 A198313 * A198315 A198316 A198317

Keyword

nonn,more,hard

Author

Jason Kimberley, Dec 12 2012

Extensions

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

Status

approved