OFFSET
0,2
COMMENTS
Also known as labeled Eulerian digraphs allowing loops. - Brendan McKay, May 12 2019
LINKS
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
KEYWORD
nonn,changed
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