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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
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.
Sequence in context: A134054 A323716 A360806 * A134086 A297566 A013175
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 April 22 20:16 EDT 2024. Contains 371906 sequences. (Running on oeis4.)