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 1-7 of 7 results.

A350794 Number of digraphs on n unlabeled nodes with a global source and sink.

Original entry on oeis.org

1, 1, 2, 20, 574, 48854, 12444800, 9849180230, 25265372689314, 218451490123178684, 6562780921564838071734, 700270642102506752862044142, 269621199012416753533007480951824, 378982029174285293421133982496722212766, 1962119228020498122395242424575089505014761082
Offset: 1

Views

Author

Andrew Howroyd, Jan 19 2022

Keywords

Links

Crossrefs

The labeled version is A350790.
Row sums of A350795.
Cf. A049531, A051421, A345258, A350360, A350796.

Programs

  • PARI
    A350794seq(15) \\ See link for program code.

A051421 Number of digraphs on n unlabeled nodes with a sink (or, with a source).

Original entry on oeis.org

1, 2, 12, 185, 8990, 1505939, 875542491, 1789247738400, 13018820342147705, 341188114831706152794, 32520852428719860881939391, 11366533535523591133597276823755, 14669006027884671703581740693080811331, 70315546525961698601351615055416574931833334
Offset: 1

Views

Author

Vladeta Jovovic

Keywords

Comments

Here a sink is defined to be a node to which all other nodes have a directed path. - Andrew Howroyd, Dec 27 2021

References

  • F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 218 (incorrect version).
  • Ronald C. Read, email to N. J. A. Sloane, 28 August, 2000.

Links

Crossrefs

The labeled case is A003028.
Row sums of A057277.
Cf. A003085, A035512, A003088, A049531, A350415, A350360, A350794.

Programs

Extensions

a(6) corrected and a(7) from Sean A. Irvine, Sep 11 2021
a(0)=1 removed and terms a(8) and beyond from Andrew Howroyd, Jan 21 2022

A350415 Number of acyclic digraphs on n unlabeled nodes with a global source (or sink).

Original entry on oeis.org

1, 1, 3, 16, 164, 3341, 138101, 11578037, 1961162564, 668678055847, 457751797355605, 628137837068751147, 1726130748679532455689, 9493834992383031007906911, 104476428350838383854529661007, 2299979227717819421763629684068904
Offset: 1

Views

Author

Andrew Howroyd, Dec 29 2021

Keywords

Comments

A local source (also called an out-node) is a node whose in-degree is zero. In the case of an acyclic digraph with only one local source, the source is also a global source.

Links

Crossrefs

The labeled case is A003025.
Row sums of A350488.
A diagonal of A122078.
Cf. A003087, A345258, A350360.

Programs

A350792 Number of digraphs on n labeled nodes with a global source (or sink).

Original entry on oeis.org

1, 2, 24, 1216, 232960, 164069376, 428074336256, 4220285062479872, 160166476125189439488, 23705806454651474422005760, 13794322751716126282614505996288, 31714534285699906476309208596247216128, 288989543377657933541050197425959169851129856
Offset: 1

Views

Author

Andrew Howroyd, Jan 16 2022

Keywords

Comments

A global sink is a node that has out-degree zero and to which all other nodes have a directed path.

Links

Crossrefs

The unlabeled version is A350360.
Row sums of A350793.
Cf. A003025, A003028, A350790.

Programs

  • PARI
    InitiallyV(15) \\ See A350793 for program code.
  • PARI
    seq(n)={my(v=vector(n)); for(n=1, n, v[n] = n*2^((n-1)^2) - sum(k=1, n-1, binomial(n,k)*2^((n-2)*(n-k))*v[k])); v}

Formula

a(n) = n*2^((n-1)^2) - Sum_{k=1..n-1} binomial(n,k)*2^((n-2)*(n-k))*a(k).

A350797 Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with k arcs and a global source (or sink), n >= 1, k = 0..(n-1)^2.

Original entry on oeis.org

1, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 4, 11, 19, 15, 8, 2, 1, 0, 0, 0, 0, 9, 45, 157, 319, 453, 455, 352, 199, 93, 32, 9, 2, 1, 0, 0, 0, 0, 0, 20, 167, 928, 3395, 9015, 18172, 29089, 37688, 40446, 36267, 27476, 17560, 9543, 4354, 1688, 547, 157, 36, 9, 2, 1
Offset: 1

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Examples

			Triangle begins:
  [1] 1;
  [2] 0, 1;
  [3] 0, 0, 2, 2,  1;
  [4] 0, 0, 0, 4, 11, 19, 15, 8, 2, 1;
  ...

Links

Crossrefs

Row sums are A350360.
Column sums are A350798.
The leading diagonal is A000081.
The labeled version is A350793.
Cf. A057277, A057278, A350795.

Programs

  • PARI
    \\ See PARI link in A350794 for program code.
{ my(A=A350797triang(5)); for(n=1, #A, print(A[n])) }

A350798 Number of unlabeled digraphs with n arcs and a global source (or sink).

Original entry on oeis.org

1, 1, 2, 6, 21, 84, 387, 1953, 10802, 64267, 408489, 2750686, 19518841, 145236878, 1128884559, 9135566309, 76758391212, 667993213393, 6008434514996, 55755719348210, 532896254763646, 5238211003916685, 52885470406233727, 547751388283907208, 5813693205313803535, 63170000832869927871
Offset: 0

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Crossrefs

Column sums of A350797.
Cf. A350360, A350752, A350796, A350906, A350907.

Programs

A351052 Number of unlabeled digraphs with n nodes containing a global sink (or source), self-loops allowed.

Original entry on oeis.org

1, 2, 18, 440, 32404, 7423456, 5473328160, 13430706072192, 113086387825668384, 3345639802029563258880, 353900830082830194441001984, 135600928084762756427776332541952, 190092581374833963606044859875698932736, 982736440685354936080688846774429648871161856
Offset: 1

Views

Author

Jim Snyder-Grant, Jan 30 2022

Keywords

Examples

			For n=3, 18 digraph edge-sets (vertex 0 is the single global sink):
  {21,10}
  {20,10}
  {22,21,10}
  {22,20,10}
  {21,12,10}
  {21,11,10}
  {20,12,10}
  {22,21,12,10}
  {22,21,11,10}
  {22,20,12,10}
  {22,20,11,10}
  {21,20,12,10}
  {21,12,11,10}
  {20,11,12,10}
  {22,21,20,12,10}
  {22,21,12,11,10}
  {22,20,12,11,10}
  {22,21,20,12,11,10}.

Links

Crossrefs

Cf. A350360 (self-loops not allowed).

Programs

  • C
    // See Jim Snyder-Grant C code to generate and count digraphs with global sinks ./gsinks -l
  • PARI
    \\ See PARI link in A350794 for program code.
seq(n)={Vec(InitiallyV(GraphCIData(n,DigraphWithLoopEdges)))} \\ Andrew Howroyd, Jan 30 2022

Extensions

Terms a(8) and beyond from Andrew Howroyd, Jan 30 2022
Showing 1-7 of 7 results.

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

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