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).

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

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Keywords

• nonn
• tabf

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

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

Crossrefs

Row sums give A049531.

Column sums give A350906.

The labeled version is A057271.

Cf. A057270, A057276, A057277, A057279, A350794, A350795.

Programs

PARI

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

Extensions

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