cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A139629 Row sums of A139624, number of 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, 2, 6, 17
Offset: 0

Views

Author

Benoit Jubin, May 01 2008

Keywords

Crossrefs

Cf. A139628, A139630.

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

Views

Author

Benoit Jubin, May 01 2008

Keywords

Comments

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.

Examples

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

Crossrefs

Cf. A136564, A139624, A139625.

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).

Original entry on oeis.org

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

Views

Author

Benoit Jubin, May 01 2008, Sep 01 2008

Keywords

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.

A136868 Table read by antidiagonals: T(n,k) is the number of 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, 2, 1, 0, 1, 2, 4, 1, 0, 1, 2, 6, 7, 1, 0, 1, 2, 6, 14, 12, 1, 0, 1, 2, 6, 17
Offset: 0

Views

Author

Benoit Jubin, May 11 2008

Keywords

Comments

Partial sums of the rows of A139624, i.e., T(n,k) = sum(T139624(n,p),p=0..k).
T(0,k) = 1 for k>=0; T(n,0) = 0 and T(n,1) = 1 for n>0.
If k>=n+1, T(n,k) = A139629(n).

Examples

			Triangle begins:
1,
1, 0,
1, 1, 0,
1, 2, 1, 0,
1, 2, 4, 1, 0,
1, 2, 6, 7, 1, 0,
1, 2, 6,14,12, 1, 0,

Crossrefs

Cf. A138352.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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