A139625 -id:A139625 - cp's OEIS frontend

A139630 Row sums of A139625, number of strongly connected directed multigraphs with loops and no vertex of degree 0, with n arcs, which are transitive (the existence of a path between two points implies the existence of an arc between those two points).

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 7, 11, 20, 30, 47, 71, 117, 201, 369, 703, 1323, 2463, 4446

Offset: 0

Benoit Jubin, May 01 2008

nonn

Cf. A139628, A139629.

A139623 Table read by rows: T(n,k) is the number of 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).

Original entry on oeis.org

1, 1, 1, 4, 3, 1, 1, 7, 12, 9, 3, 1, 1, 13

Offset: 1

Benoit Jubin, May 01 2008

Length of the n^th row: 2n.
T(n,1) = T(n,2n) = 1 and T(n,2n-1) = 3 if n>1.
Row sums: A139628.

			Triangle begins
1, 1;
1, 4, 3, 1;
1, 7, 12, 9, 3, 1;

Cf. A136564, A139624, A139625.

A139624 Table read by rows: T(n,k) is the number of 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).

Original entry on oeis.org

1, 1, 1, 3, 2, 1, 6, 7, 3, 1, 11

Offset: 1

Benoit Jubin, May 01 2008

Length of the n-th row: n+1.
T(n,1) = 1
Row sums: A139629.

			Triangle begins
1;
1, 1;
3, 2, 1;
6, 7, 3, 1;

Cf. A139623, A139625.

A143842 Table read by antidiagonals: T(n,k) is the number of strongly connected directed multigraphs with loops 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).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 2, 3, 1, 0, 1, 1, 1, 1, 2, 3, 7, 1, 0, 1, 1, 1, 1, 2, 3, 7, 11, 1, 0, 1, 1, 1, 1, 2, 3, 7, 11, 20, 1, 0, 1, 1, 1, 1, 2, 3, 7, 11, 20, 29, 1, 0, 1, 1, 1, 1, 2, 3, 7, 11, 20, 30, 45, 1, 0, 1, 1, 1, 1, 2, 3, 7, 11, 20

Offset: 0

Benoit Jubin, Sep 02 2008

Partial sums of the rows of A139625, i.e., T(n,k) = sum(T139625(n,p),p=0..k).

If k>=floor(sqrt(n)), T(n,k) = A139630(n).

Cf. A138352, A136868, A143841.

cp's OEIS Frontend

A139630 Row sums of A139625, number of strongly connected directed multigraphs with loops and no vertex of degree 0, with n arcs, which are transitive (the existence of a path between two points implies the existence of an arc between those two points).

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A139623 Table read by rows: T(n,k) is the number of 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).

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A139624 Table read by rows: T(n,k) is the number of 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).

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A143842 Table read by antidiagonals: T(n,k) is the number of strongly connected directed multigraphs with loops 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).

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Keywords

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