A008325 Number of simple regular trivalent bipartite graphs with 2n nodes.

1, 1, 2, 6, 14, 41, 157, 725, 4196, 29816, 246644, 2297075, 23503477, 260265023, 3090336300, 39101547971, 524782945991, 7443247863498, 111221983956652, 1746165682538497, 28734206614035245, 494526496354065244, 8883865784392246280, 166286434745252091055, 3237719048384605059117, 65477287940472122129194

Offset: 3

Author

Brendan McKay

Keywords

• nonn
• hard

Comments

Euler transform of A006823. - Peter J. Taylor, Sep 28 2017

Links

• G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.
• Sean A. Irvine, On the difference between A004066 and A008325

Crossrefs

Column k=3 of A008327.

Cf. A004066 (bicolored), A006823 (connected).

Programs

Mathematica

A006823 = Cases[Import["https://oeis.org/A006823/b006823.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];
b[n_] := If[n >= 3, A006823[[n - 2]], 0];
a = etr[b];
a /@ Range[3, 16] (* Jean-François Alcover, Dec 03 2019 *)

Extensions

a(15)-a(16) from Peter J. Taylor, Sep 28 2017

Terms a(17) and beyond from Andrew Howroyd, Apr 03 2020