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

1,7

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.

Links

Table of n, a(n) for n=1..47.

Example

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

Crossrefs

Cf. A139623, A139624.

Sequence in context: A191093 A266303 A267354 * A053785 A233809 A207536

Adjacent sequences: A139622 A139623 A139624 * A139626 A139627 A139628

Keyword

nonn,tabf

Author

Benoit Jubin, May 01 2008, Sep 01 2008

Status

approved