A057279 -id:A057279 - cp's OEIS frontend

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

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

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

			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.

Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)

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

\\ See PARI link in A350489 for program code.
{ my(A=A057276rows(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 13 2022

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

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

			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.

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

Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)

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

\\ See PARI link in A350794 for program code.
{ my(A=A057278triang(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 21 2022

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

A057277 Triangle T(n,k) of number of digraphs with a source on n unlabeled nodes with k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 0, 1, 1, 0, 0, 2, 4, 4, 1, 1, 0, 0, 0, 4, 16, 34, 46, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 9, 56, 229, 573, 1058, 1448, 1653, 1487, 1153, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 20, 198, 1218, 5089, 15596, 37302, 72776, 119531, 168233, 205923, 220337, 207147, 170965, 124099, 78811, 43861, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1

Offset: 1

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

			Triangle begins:
  [1],
  [0, 1, 1],
  [0, 0, 2, 4, 4, 1, 1],
  [0, 0, 0, 4, 16, 34, 46, 38, 27, 13, 5, 1, 1],
  ....
The number of digraphs with a source on 3 unlabeled nodes is 12 = 2+4+4+1+1.

Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)

Row sums give A051421.
Column sums give A350907.
The labeled version is A057274.
Cf. A057270, A057276, A057278, A057279, A350794, A350797.

\\ See PARI link in A350794 for program code.
{ my(A=A057277triang(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 21 2022

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

Vladeta Jovovic, Goran Kilibarda, Aug 23 2000

			[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.

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

R. W. Robinson, Counting strong digraphs (research announcement), J. Graph Theory 1, 1977, pp. 189-190.

Row sums give A003088. Cf. A057271-A057279.

More terms from Sean A. Irvine, May 27 2022

A057272 Triangle T(n,k) of number of digraphs with a quasi-source on n labeled nodes and with k arcs, k=0,1,..,n*(n-1).

Original entry on oeis.org

1, 0, 2, 1, 0, 0, 12, 20, 15, 6, 1, 0, 0, 0, 104, 426, 768, 920, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 1160, 9184, 32420, 73000, 123425, 166860, 184426, 167900, 125965, 77520, 38760, 15504, 4845, 1140, 190, 20, 1

Offset: 1

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

			Triangle starts:
1;
0,2,1;
0,0,12,20,15,6,1;
0,0,0,104,426,768,920,792,495,220,66,12,1;
...
Number of digraphs with a quasi-source on 3 labeled nodes is 54=12+20+15+6+1.

V. Jovovic and G. Kilibarda, Enumeration of labeled quasi-initially connected digraphs, Discrete Math., 224 (2000), 151-163.

Row sums give A049414. Cf. A057270, A057271, A057273-A057279.

cp's OEIS Frontend

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

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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).

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A057277 Triangle T(n,k) of number of digraphs with a source on n unlabeled nodes with k arcs, k=0..n*(n-1).

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

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A057272 Triangle T(n,k) of number of digraphs with a quasi-source on n labeled nodes and with k arcs, k=0,1,..,n*(n-1).

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