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

0,8

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.

Example

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;
  ...

Prog

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

Crossrefs

Row sums give A003087.

Diagonals include A000007, A350415.

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

Sequence in context: A340986 A340798 A355427 * A292783 A320354 A285320

Adjacent sequences: A122075 A122076 A122077 * A122079 A122080 A122081

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 18 2006

Extensions

Zero terms inserted by Andrew Howroyd, Dec 29 2021

Status

approved