A229865 Number of n X n 0..1 arrays with corresponding row and column sums equal.

1, 2, 8, 80, 2432, 247552, 88060928, 112371410944, 523858015518720, 9041009511609073664, 583447777113052431515648, 141885584718620229407228821504, 130832005909904417592540055577034752, 459749137931232137234615429529864283095040, 6182706200522446492946534924719926752508110700544

Offset

0,2

Comments

Also known as labeled Eulerian digraphs allowing loops. - Brendan McKay, May 12 2019

Links

Table of n, a(n) for n=0..14.

Mohammad Behzad Kang and Andrew Salch, The mod p cohomology of the Morava stabilizer group at large primes, arXiv:2410.24171 [math.AT], 2024. See p. 46.

Formula

a(n) = 2^n * A007080(n). - Andrew Howroyd, Sep 11 2019

Example

Some solutions for n=4:
  0 0 0 1     0 0 1 0     0 0 0 1     0 0 1 0     0 0 1 1
  0 1 0 0     1 0 0 0     1 0 1 0     0 0 1 1     1 0 0 1
  0 0 0 1     0 1 0 0     0 1 0 1     0 1 1 1     1 1 1 0
  1 0 1 0     0 0 0 1     0 1 1 0     1 1 0 0     0 1 1 1
From Gus Wiseman, Jun 22 2019: (Start)
The a(3) = 8 Eulerian digraph edge-sets:
  {}
  {11}
  {22}
  {11,22}
  {12,21}
  {11,12,21}
  {12,21,22}
  {11,12,21,22}
(End)

Mathematica

Table[Length[Select[Subsets[Tuples[Range[n], 2]], Sort[First/@#]==Sort[Last/@#]&]], {n, 4}] (* Gus Wiseman, Jun 22 2019 *)

Crossrefs

Column 1 of A229870.

The unlabeled version is A308111.

Cf. A000595, A002416, A002720, A007080.

Cf. A326209, A326237, A326251, A326252, A326253.

Sequence in context: A134054 A323716 A360806 * A134086 A297566 A013175

Adjacent sequences: A229862 A229863 A229864 * A229866 A229867 A229868

Keyword

nonn

Author

R. H. Hardin, Oct 01 2013

Extensions

a(0)=1 prepended by Alois P. Heinz, May 14 2019

Terms a(11) and beyond from Andrew Howroyd, Sep 11 2019

Status

approved