
MATHEMATICA

dinorm[m_]:=If[m=={}, {}, If[Union@@m!=Range[Max@@Flatten[m]], dinorm[m/. Apply[Rule, Table[{(Union@@m)[[i]], i}, {i, Length[Union@@m]}], {1}]], First[Sort[dinorm[m, 1]]]]];
dinorm[m_, aft_]:=If[Length[Union@@m]<=aft, {m}, With[{mx=Table[Count[m, i, {2}], {i, Select[Union@@m, #1>=aft&]}]}, Union@@(dinorm[#1, aft+1]&)/@Union[Table[Map[Sort, m/. {par+aft1>aft, aft>par+aft1}, {0}], {par, First/@Position[mx, Max[mx]]}]]]];
Table[Length[Select[Union[dinorm/@Subsets[Tuples[Range[n], 2]]], FindHamiltonianCycle[Graph[Range[n], DirectedEdge@@@#]]!={}&]], {n, 0, 4}] (* Mathematica 8.0+. Warning: Using HamiltonianGraphQ instead of FindHamiltonianCycle returns a(4) = 867 which is incorrect *)


CROSSREFS

The labeled case is A326204.
The case without loops is A326225.
The undirected case is A003216 (without loops) or A326215 (with loops).
Unlabeled nonHamiltonian digraphs are A326223.
Unlabeled digraphs with a Hamiltonian path are A326221.
Cf. A000595, A002416, A003087, A057864, A246446, A326208.
Sequence in context: A013312 A013318 A193338 * A291262 A307922 A048674
Adjacent sequences: A326223 A326224 A326225 * A326227 A326228 A326229
