A185336 Number of not necessarily connected 3-regular simple graphs on 2n vertices with girth at least 6.

1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624502, 122090545, 3328929960, 93990692632, 2754222605808

Offset: 0

Author

Jason Kimberley, Jan 28 2012

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, 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 6: A014374 (connected), A185236 (disconnected), this sequence (not necessarily connected).

Not necessarily connected k-regular simple graphs with girth at least 6: A185326 (k=2), this sequence (k=3).

Not necessarily connected 3-regular simple graphs with girth *at least* g: A005638 (g=3), A185334 (g=4), A185335 (g=5), this sequence (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

A014374 = Cases[Import["https://oeis.org/A014374/b014374.txt", "Table"], {, }][[All, 2]];
etr[f_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d f[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
a = etr[A014374[[# + 1]]&];
a /@ Range[0, Length[A014374] - 1] (* Jean-François Alcover, Dec 04 2019 *)

Formula

Euler transformation of A014374.

Extensions

a(18) from A014374 from Jean-François Alcover, Dec 04 2019