A229865 - OEIS

%I #32 Nov 07 2024 03:55:50

%S 1,2,8,80,2432,247552,88060928,112371410944,523858015518720,

%T 9041009511609073664,583447777113052431515648,

%U 141885584718620229407228821504,130832005909904417592540055577034752,459749137931232137234615429529864283095040,6182706200522446492946534924719926752508110700544

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

%C Also known as labeled Eulerian digraphs allowing loops. - _Brendan McKay_, May 12 2019

%H Mohammad Behzad Kang and Andrew Salch, <a href="https://arxiv.org/abs/2410.24171">The mod p cohomology of the Morava stabilizer group at large primes</a>, arXiv:2410.24171 [math.AT], 2024. See p. 46.

%F a(n) = 2^n * A007080(n). - _Andrew Howroyd_, Sep 11 2019

%e Some solutions for n=4:

%e   0 0 0 1     0 0 1 0     0 0 0 1     0 0 1 0     0 0 1 1

%e   0 1 0 0     1 0 0 0     1 0 1 0     0 0 1 1     1 0 0 1

%e   0 0 0 1     0 1 0 0     0 1 0 1     0 1 1 1     1 1 1 0

%e   1 0 1 0     0 0 0 1     0 1 1 0     1 1 0 0     0 1 1 1

%e From _Gus Wiseman_, Jun 22 2019: (Start)

%e The a(3) = 8 Eulerian digraph edge-sets:

%e   {}

%e   {11}

%e   {22}

%e   {11,22}

%e   {12,21}

%e   {11,12,21}

%e   {12,21,22}

%e   {11,12,21,22}

%e (End)

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

%Y Column 1 of A229870.

%Y The unlabeled version is A308111.

%Y Cf. A000595, A002416, A002720, A007080.

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

%K nonn

%O 0,2

%A _R. H. Hardin_, Oct 01 2013

%E a(0)=1 prepended by _Alois P. Heinz_, May 14 2019

%E Terms a(11) and beyond from _Andrew Howroyd_, Sep 11 2019