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.

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

A057276 Triangle T(n,k) of number of strongly connected digraphs on n unlabeled nodes and with k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 4, 16, 22, 22, 11, 5, 1, 1, 0, 0, 0, 0, 0, 1, 7, 58, 240, 565, 928, 1065, 953, 640, 359, 150, 59, 16, 5, 1, 1, 0, 0, 0, 0, 0, 0, 1, 10, 165, 1281, 6063, 19591, 47049, 87690, 131927, 163632, 170720, 151238, 115122, 75357, 42745, 20891, 8877, 3224, 1039, 286, 76, 17, 5, 1, 1
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Keywords

Examples

			Triangle begins:
  [1] 1;
  [2] 0,0,1;
  [3] 0,0,0,1,2,1,1;
  [4] 0,0,0,0,1,4,16,22,22,11,5,1,1;
  ...
The number of strongly connected digraphs on 3 unlabeled nodes is 5 = 1+2+1+1.

Links

Crossrefs

Row sums give A035512.
Column sums give A350752.
The labeled version is A057273.
Cf. A054733, A057270, A057277, A057278, A057279, A350489.

Programs

Extensions

Terms a(46) and beyond from Andrew Howroyd, Jan 13 2022

A057278 Triangle T(n,k) of number of digraphs with a source and a sink on n unlabeled nodes and 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, 11, 31, 45, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 1, 23, 152, 486, 992, 1419, 1641, 1485, 1152, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 1, 42, 517, 3194, 12174, 32860, 68423, 116168, 166164, 204867, 219906, 206993, 170922, 124088, 78809, 43860, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Keywords

Examples

			Triangle begins:
  [1],
  [0,1,1],
  [0,0,1,4,4,1,1],
  [0,0,0,1,11,31,45,38,27,13,5,1,1],
  ...
The number of digraphs with a source and a sink on 3 unlabeled nodes is 11 = 1+4+4+1+1.

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 give A049531.
Column sums give A350906.
The labeled version is A057271.
Cf. A057270, A057276, A057277, A057279, A350794, A350795.

Programs

Extensions

Terms a(46) and beyond from Andrew Howroyd, Jan 21 2022

A057274 Triangle T(n,k) of the number of digraphs with a source on n labeled nodes with k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 0, 2, 1, 0, 0, 9, 20, 15, 6, 1, 0, 0, 0, 64, 330, 720, 914, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 625, 5804, 24560, 63940, 117310, 164260, 183716, 167780, 125955, 77520, 38760, 15504, 4845, 1140, 190, 20, 1
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Keywords

Examples

			Triangle begins:
  1;
  0, 2, 1;
  0, 0, 9, 20,  15,   6,   1;
  0, 0, 0, 64, 330, 720, 914, 792, 495, 220, 66, 12, 1;
  ...
The number of digraphs with a source on 3 labeled nodes is the sum of the terms in row 3, i.e., 0+0+9+20+15+6+1 = 51 = A003028(3).

Links

Crossrefs

Row sums give A003028.
The unlabeled version is A057277.
Cf. A057271, A057272, A057273, A057275, A062735.

Programs

  • PARI
    \\ See A057273 for Strong.
Lambda(t, nn, e=2)={my(v=vector(1+nn)); for(n=0, nn, v[1+n] = e^(n*(n+t-1)) - sum(k=0, n-1, binomial(n,k)*e^((n-1)*(n-k))*v[1+k])); v}
Initially(n, e=2)={my(s=Strong(n, e), v=vector(n)); for(k=1, n, my(u=Lambda(k, n-k, e)); for(i=k, n, v[i] += binomial(i,k)*u[1+i-k]*s[k])); v }
row(n)={ Vecrev(Initially(n, 1+'y)[n]) }
{ for(n=1, 5, print(row(n))) } \\ Andrew Howroyd, Jan 11 2022

A350795 Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with k arcs and a global source and sink, n >= 1, k = 0..max(1,n-1)*(n-2)+1.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 6, 8, 4, 1, 0, 0, 0, 0, 1, 16, 70, 140, 159, 113, 53, 17, 4, 1, 0, 0, 0, 0, 0, 1, 33, 313, 1439, 3941, 7297, 9750, 9840, 7717, 4788, 2377, 946, 309, 80, 18, 4, 1, 0, 0, 0, 0, 0, 0, 1, 58, 998, 8447, 43269, 152135, 396011
Offset: 1

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Examples

			Triangle begins:
  [1] 1;
  [2] 0, 1;
  [3] 0, 0, 1, 1;
  [4] 0, 0, 0, 1, 6,  8,  4,   1;
  [5] 0, 0, 0, 0, 1, 16, 70, 140, 159, 113, 53, 17, 4, 1;
  ...

Links

Crossrefs

Row sums are A350794.
Column sums are A350796.
The labeled version is A350791.
Cf. A057277, A057278, A350797.

Programs

  • PARI
    \\ See PARI link in A350794 for program code.
{ my(A=A350795triang(5)); for(n=1, #A, print(A[n])) }

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])) }

A350907 Number of unlabeled initially connected digraphs with n arcs.

Original entry on oeis.org

1, 1, 3, 8, 29, 111, 522, 2604, 14459, 85796, 544753, 3659313, 25902251, 192171887, 1489090036, 12011329453, 100583184087, 872346402439, 7819597099285, 72313198682817, 688784601395670, 6747614973580663, 67896777481378196, 700913648767703716, 7415270780191604414, 80316990564932960558
Offset: 0

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Crossrefs

Column sums of A057277.
Cf. A051421 (by vertices), A350752, A350796, A350798, A350906.

Programs

Showing 1-7 of 7 results.

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

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