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.

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A138352 Table read by antidiagonals: T(n,k) is the number of transitive directed multigraphs with loops with n arcs and k vertices.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 5, 1, 0, 1, 2, 8, 8, 1, 0, 1, 2, 9, 20, 14, 1, 0, 1, 2, 9, 29
Offset: 0

Views

Author

Benoit Jubin, May 07 2008

Keywords

Comments

Partial sums of the rows of A139623, i.e., T(n,k) = sum(T139623(n,p),p=0..k).
If k>=2n, T(n,k) = A139628(n).

Crossrefs

Cf. A138107.

A144047 Limiting values of A136564.

Original entry on oeis.org

1, 4, 22, 111, 570, 2917, 15112, 78900, 416525, 2221529, 11974498, 65211746, 358742016, 1992975905, 11178149883, 63279615534, 361464920864, 2082869242399, 12104344580384, 70924864962233, 418922049779244
Offset: 0

Views

Author

Benoit Jubin and Vladeta Jovovic, Sep 08 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ Needs G function from A138107.
    a(n)={if(n==0, 1, my(m=2*n); polcoef(G(3*n, x + O(x*x^m)) - G(3*n-1, x + O(x*x^m)), m))} \\ Andrew Howroyd, Apr 20 2020

Formula

a(n) = A136564(2*n, 3*n) for n > 0. - Andrew Howroyd, Apr 20 2020

Extensions

Offset corrected and a(7)-a(20) from Andrew Howroyd, Apr 20 2020

A362387 Number of directed multigraphs including self-loops on n vertices and n edges.

Original entry on oeis.org

1, 1, 6, 31, 198, 1270, 8838, 63419, 475796, 3697876, 29793899, 248312750, 2139071800, 19023864211, 174495408060, 1648972635108, 16036927429350, 160338342813918, 1646265278973845, 17340402062779049, 187190960572134321
Offset: 0

Views

Author

Marko Riedel, Jun 09 2023

Keywords

Examples

			For n=2 we have two edges and two vertices, for a total of six graphs:
* one vertex with two loops attached to it
* one loop attached to each vertex
* two vertices linked by two edges in opposite directions
* two vertices linked by two edges in the same direction
* one vertex with a loop being pointed at
* one vertex with a loop being pointed away from.
		

References

  • F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973, page 88.

Crossrefs

Main diagonal of A138107.

Formula

a(n) = A138107(n,n).
Previous Showing 11-13 of 13 results.