A185334 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 4.

1, 0, 0, 1, 2, 6, 23, 112, 801, 7840, 97723, 1436873, 23791155, 432878091, 8544173926, 181519645163, 4127569521160

Offset: 0

Author

Jason Kimberley, Feb 15 2011

Keywords

• nonn
• more
• hard

Comments

The null graph on 0 vertices is vacuously 3-regular; since it is acyclic, it has infinite girth.

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

3-regular simple graphs with girth at least 4: A014371 (connected), A185234 (disconnected), this sequence (not necessarily connected).

Not necessarily connected k-regular simple graphs with girth at least 4: A185314 (any k), A185304 (triangle); specified degree k: A008484 (k=2), this sequence (k=3), A185344 (k=4), A185354 (k=5), A185364 (k=6).

Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), this sequence (g=4), A185335 (g=5), A185336 (g=6).

Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Programs

Mathematica

A014371 = Cases[Import["https://oeis.org/A014371/b014371.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A014371] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Formula

Euler transformation of A014371.