cp's OEIS Frontend

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

%I A229865 #32 Nov 07 2024 03:55:50
%S A229865 1,2,8,80,2432,247552,88060928,112371410944,523858015518720,
%T A229865 9041009511609073664,583447777113052431515648,
%U A229865 141885584718620229407228821504,130832005909904417592540055577034752,459749137931232137234615429529864283095040,6182706200522446492946534924719926752508110700544
%N A229865 Number of n X n 0..1 arrays with corresponding row and column sums equal.
%C A229865 Also known as labeled Eulerian digraphs allowing loops. - _Brendan McKay_, May 12 2019
%H A229865 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 A229865 a(n) = 2^n * A007080(n). - _Andrew Howroyd_, Sep 11 2019
%e A229865 Some solutions for n=4:
%e A229865   0 0 0 1     0 0 1 0     0 0 0 1     0 0 1 0     0 0 1 1
%e A229865   0 1 0 0     1 0 0 0     1 0 1 0     0 0 1 1     1 0 0 1
%e A229865   0 0 0 1     0 1 0 0     0 1 0 1     0 1 1 1     1 1 1 0
%e A229865   1 0 1 0     0 0 0 1     0 1 1 0     1 1 0 0     0 1 1 1
%e A229865 From _Gus Wiseman_, Jun 22 2019: (Start)
%e A229865 The a(3) = 8 Eulerian digraph edge-sets:
%e A229865   {}
%e A229865   {11}
%e A229865   {22}
%e A229865   {11,22}
%e A229865   {12,21}
%e A229865   {11,12,21}
%e A229865   {12,21,22}
%e A229865   {11,12,21,22}
%e A229865 (End)
%t A229865 Table[Length[Select[Subsets[Tuples[Range[n],2]],Sort[First/@#]==Sort[Last/@#]&]],{n,4}] (* _Gus Wiseman_, Jun 22 2019 *)
%Y A229865 Column 1 of A229870.
%Y A229865 The unlabeled version is A308111.
%Y A229865 Cf. A000595, A002416, A002720, A007080.
%Y A229865 Cf. A326209, A326237, A326251, A326252, A326253.
%K A229865 nonn
%O A229865 0,2
%A A229865 _R. H. Hardin_, Oct 01 2013
%E A229865 a(0)=1 prepended by _Alois P. Heinz_, May 14 2019
%E A229865 Terms a(11) and beyond from _Andrew Howroyd_, Sep 11 2019