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

0,10

Comments

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

Links

Table of n, a(n) for n=0..18.

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

Formula

Euler transformation of A014374.

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 *)

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).

Sequence in context: A006926 A185136 A014374 * A125709 A363314 A203112

Adjacent sequences: A185333 A185334 A185335 * A185337 A185338 A185339

Keyword

nonn,more,hard

Author

Jason Kimberley, Jan 28 2012

Extensions

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

Status

approved