A004066 -id:A004066 - cp's OEIS frontend

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

Brendan McKay

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

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

Column k=3 of A008327.

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

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 *)

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

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

A000840 Number of cubic bicolored graphs on n unlabeled nodes admitting an automorphism exchanging the colors.

Original entry on oeis.org

0, 0, 1, 1, 2, 5, 12, 31, 90, 285, 938, 3285, 11983, 45390, 177803, 718390, 2986407, 12749364, 55802982, 250068732, 1145923828, 5363795830, 25620207380, 124767647097, 618983876918, 3126035142910, 16060182735947, 83883575376862, 445164927249466, 2399098651337048

Offset: 1

Brendan McKay and Eric Rogoyski

nonn

Column k=3 of A333159.

Cf. A000512, A000843, A004066, A008325.

a(11)-a(30) from Andrew Howroyd, Mar 10 2020

A333732 Number of non-isomorphic n X n binary matrices with equal row and column sums up to permutation of rows and columns and transposition.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 18, 40, 230, 4296, 431206, 162267272, 201636689772, 777816803942188, 9865957936943931980, 395886667549681689592056, 53716176608076643470621240097, 23524515269630339982914646822137232, 35682168849414944013547274452501783251521

Offset: 0

Andrew Howroyd, Apr 03 2020

nonn

Number of simple regular bicolored graphs on 2n unlabeled nodes and allowing the color classes to be interchanged.

First differs from A008324 at n=12. See the note in A004066 by Sean A. Irvine for an explanation of why these two sequences are different.

Cf. A004066, A008324, A333160, A333681.

a(n) = (A333160(n) + A333681(n)) / 2.

a(n) >= A008324(n).

cp's OEIS Frontend

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

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A000840 Number of cubic bicolored graphs on n unlabeled nodes admitting an automorphism exchanging the colors.

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A333732 Number of non-isomorphic n X n binary matrices with equal row and column sums up to permutation of rows and columns and transposition.

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