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 1-6 of 6 results.

A039747 Erroneous version of A003088.

Original entry on oeis.org

1, 1, 2, 11, 172, 8603, 1478644
Offset: 0

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Author

Keywords

References

  • F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 218.

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

A049531 Number of digraphs with a source and a sink on n unlabeled nodes.

Original entry on oeis.org

1, 2, 11, 173, 8675, 1483821, 870901739, 1786098545810, 13011539185371716, 341128981258340797839, 32519138088689298538132027, 11366354205366488038532562993809, 14668937734550708660348161757913398001, 70315451107713339843384354196009678853303102
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

Comments

Here a source is defined to be a node which has a directed path to all other nodes and a sink to be a node to which all other nodes have a directed path. A digraph with a source and a sink can also be described as initially-finally connected. - Andrew Howroyd, Jan 01 2022

References

  • V. Jovovic, G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996), p. 246.

Links

Crossrefs

Row sums of A057278.
The labeled version is A049524.
Cf. A003085, A035512, A003088, A051421, A345258, A350794.

Programs

Extensions

a(6)-a(7) from Andrew Howroyd, Jan 01 2022
Terms a(8) and beyond from Andrew Howroyd, Jan 20 2022

A057270 Triangle T(n,k) of number of unilaterally connected digraphs on n unlabeled nodes with k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 0, 1, 1, 0, 0, 1, 4, 4, 1, 1, 0, 0, 0, 1, 10, 30, 45, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 1, 20, 136, 462, 972, 1412, 1639, 1485, 1152, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 1, 35, 437, 2833, 11325, 31615, 67207, 115344, 165762, 204723, 219866, 206986, 170920, 124088, 78809, 43860, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Aug 23 2000

Keywords

Examples

			[1],[0,1,1],[0,0,1,4,4,1,1],[0,0,0,1,10,30,45,38,27,13,5,1,1],...; Number of unilaterally connected digraphs on 4 unlabeled nodes is 171=1+10+30+45+38+27+13+5+1+1.

References

  • F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.

Links

Crossrefs

Row sums give A003088. Cf. A057271-A057279.

Extensions

More terms from Sean A. Irvine, May 27 2022

A003029 Number of unilaterally connected digraphs with n labeled nodes.

Original entry on oeis.org

1, 3, 48, 3400, 955860, 1034141596, 4340689156440, 71756043154026904, 4716284688998245793376, 1237457313794197125403483936, 1297922676419612772784598299454784, 5444329780242560941321703550018388707904, 91342929096228825123968637168641318872709897472
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • V. Jovovic, G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996), 237-247.
  • R. W. Robinson, Counting labeled acyclic digraphs, pp. 239-273 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

The unlabeled version is A003088.
Row sums of A057275.
Cf. A003027, A003028, A003030, A049524, A049414.

Programs

Extensions

Corrected and extended by Vladeta Jovovic, Goran Kilibarda
Terms a(12) and beyond from Andrew Howroyd, Jan 11 2022

A049512 Number of quasi-initially connected digraphs on n unlabeled nodes.

Original entry on oeis.org

1, 2, 13, 197, 9312, 1528634, 880277970
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

Comments

From Sean A. Irvine, Aug 01 2021: (Start)
A quasi-initially connected digraph is a digraph containing at least one vertex v such that every vertex u in the graph can either be reached from v or v can be reached from u (while obeying the directions on the edges).
There is no known formula. (End)

Links

Crossrefs

Cf. A049414, A003085, A035512, A003088, A051421.

Extensions

a(6)-a(7) from Sean A. Irvine, Aug 01 2021
Showing 1-6 of 6 results.

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

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