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A229865 Number of n X n 0..1 arrays with corresponding row and column sums equal. 9
1, 2, 8, 80, 2432, 247552, 88060928, 112371410944, 523858015518720, 9041009511609073664, 583447777113052431515648, 141885584718620229407228821504, 130832005909904417592540055577034752, 459749137931232137234615429529864283095040, 6182706200522446492946534924719926752508110700544 (list; graph; refs; listen; history; text; internal format)
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.

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: A289897 A134054 A323716 * 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

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Last modified October 20 22:37 EDT 2019. Contains 328291 sequences. (Running on oeis4.)