A122078 Triangle read by rows: T(n,k) is the number of unlabeled acyclic digraphs with n >= 0 nodes and n-k outnodes (0 <= k <= n).

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 11, 16, 0, 1, 4, 25, 108, 164, 0, 1, 5, 47, 422, 2168, 3341, 0, 1, 6, 78, 1251, 15484, 88747, 138101, 0, 1, 7, 120, 3124, 79836, 1215783, 7409117, 11578037, 0, 1, 8, 174, 6925, 333004, 11620961, 199203464, 1252610909, 1961162564, 0

Offset: 0

Author

N. J. A. Sloane, Oct 18 2006

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins:
  1:
  1, 0;
  1, 1,  0;
  1, 2,  3,    0;
  1, 3, 11,   16,     0;
  1, 4, 25,  108,   164,     0;
  1, 5, 47,  422,  2168,  3341,      0;
  1, 6, 78, 1251, 15484, 88747, 138101, 0;
  ...
		

References

• R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..495 (rows 0..30; rows 0..15 from R. W. Robinson)
• Andrew Howroyd, PARI program, Dec 2021, updated Jan 2022.

Crossrefs

Row sums give A003087.

Diagonals include A000007, A350415.

Cf. A058876 (labeled case), A350447, A350448, A350449, A350450.

Programs

PARI

\\ See link for program code.
{ my(T=AcyclicDigraphsByNonSources(8)); for(n=1, #T, print(T[n])) } \\ Andrew Howroyd, Dec 31 2021

Extensions

Zero terms inserted by Andrew Howroyd, Dec 29 2021