A008323 -id:A008323 - cp's OEIS frontend

A008326 Triangle read by rows: T(n,k) is the number of simple regular connected bipartite graphs with 2n nodes and degree k, (2 <= k <= n).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 4, 1, 1, 1, 13, 14, 4, 1, 1, 1, 38, 129, 41, 7, 1, 1, 1, 149, 1980, 1981, 157, 8, 1, 1, 1, 703, 62611, 304495, 62616, 725, 12, 1, 1, 1, 4132, 2806490, 78322915, 78322916, 2806508, 4196, 14, 1, 1, 1, 29579, 158937213, 27033154060, 147252447227, 27033154065, 158937367, 29817, 21, 1, 1

Offset: 2

Brendan McKay and Eric Rogoyski

This sequence can be derived from A133687 and A333159. In particular, if w(n) is the inverse Euler transform of column k of A133687 and s(n) is the inverse Euler transform of column k of A333159, then 2*T(2*n+1,k) = w(2*n+1) + s(2*n+1) and 2*T(2*n,k) = w(2*n) + s(2*n) - w(n) + T(n,k). - Andrew Howroyd, Apr 03 2020

			Triangle begins:
  1;
  1,   1;
  1,   1,    1;
  1,   2,    1,    1;
  1,   5,    4,    1,   1;
  1,  13,   14,    4,   1, 1;
  1,  38,  129,   41,   7, 1, 1;
  1, 149, 1980, 1981, 157, 8, 1, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 2..154
B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Columns k=3..7 are A006823, A006824, A006825, A014385, A014387.
Row sums are in A008323.
Cf. A008327, A133687, A333159.

More terms from Eric Rogoyski, May 15 1997
Name clarified by Andrew Howroyd, Sep 05 2018
Terms a(55) and beyond from Andrew Howroyd, Apr 03 2020

A008324 Number of simple regular bipartite graphs with 2n nodes.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 18, 40, 230, 4296, 431206, 162267272, 201636689771, 777816803942186, 9865957936943931964, 395886667549681689591841, 53716176608076643470621234239, 23524515269630339982914646821899537, 35682168849414944013547274452501768506834

Offset: 0

Brendan McKay

First differs from A333732 at n = 12. - Andrew Howroyd, Apr 03 2020

Brendan McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Row sums of A008327.

Cf. A033995, A008323, A333732.

a(0)=1 prepended and terms a(11) and beyond from Andrew Howroyd, Apr 03 2020

A087114 Number of regular bipartite simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 4, 1, 6, 1, 8, 1, 18, 1, 40, 1, 230, 1, 4296, 1, 431206, 1, 162267272, 1, 201636689771, 1, 777816803942186, 1, 9865957936943931964, 1, 395886667549681689591841, 1, 53716176608076643470621234239, 1, 23524515269630339982914646821899537, 1, 35682168849414944013547274452501768506834, 1

Offset: 0

Eric W. Weisstein, Aug 13 2003

nonn

A graph must be regular and bipartite to be a semisymmetric graph.

Eric Weisstein's World of Mathematics, Semisymmetric Graph

Cf. A008323, A008324, A008327.

a(2*n + 1) = 1, a(2*n) = A008324(n). - Andrew Howroyd, Sep 05 2018

a(10)-a(19) from Andrew Howroyd, Sep 05 2018

a(0)=1 prepended and a(20) onwards added by Andrew Howroyd, Feb 21 2024

cp's OEIS Frontend

A008326 Triangle read by rows: T(n,k) is the number of simple regular connected bipartite graphs with 2n nodes and degree k, (2 <= k <= n).

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A008324 Number of simple regular bipartite graphs with 2n nodes.

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A087114 Number of regular bipartite simple graphs on n nodes.

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