A139625 Table read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops and no vertex of degree 0, with n arcs and k vertices, which are transitive (the existence of a path between two points implies the existence of an arc between those two points).

1, 1, 1, 1, 1, 1, 2, 1, 6, 1, 10, 1, 19, 1, 28, 1, 1, 44, 2, 1, 60, 10, 1, 85, 31, 1, 110, 90, 1, 146, 222, 1, 182, 520, 1, 231, 1090, 1, 1, 280, 2180, 2, 1, 344, 4090, 11, 1

Offset: 1

Author

Benoit Jubin, May 01 2008, Sep 01 2008

Keywords

• nonn
• tabf

Comments

Length of the n^th row: floor(sqrt(n)).

These graphs are reflexive (each vertex has a self-loop), so T(n,k) = sum(A139621(n-k^2,m),m=0..k)

T(n,1) = 1, T(n,2) = A005993(n-4), T(n,3) = A050927(n-9), T(n,4) = A050929(n-16).

Row sums: A139630.

Examples

			Triangle begins:
  1
  1
  1
  1  1
  1  2
  1  6
  1 10
  1 19
  1 28  1
		

Crossrefs

Cf. A139623, A139624.