A350447 Triangle read by rows: T(n,k) is the number of acyclic digraphs on n unlabeled nodes with k arcs, n >=0, k = 0..(n-1)*n/2.

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 4, 9, 9, 6, 1, 1, 1, 4, 12, 37, 60, 80, 63, 33, 10, 1, 1, 1, 4, 13, 51, 163, 407, 796, 1169, 1291, 1057, 649, 281, 85, 15, 1, 1, 1, 4, 13, 54, 215, 846, 2690, 7253, 15703, 27596, 39057, 44902, 41723, 31336, 18844, 8983, 3325, 920, 180, 21, 1

Offset

0,7

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1350 (rows 0..20)

Example

Triangle begins:
  [0] 1;
  [1] 1;
  [2] 1, 1;
  [3] 1, 1, 3,  1;
  [4] 1, 1, 4,  9,  9,  6,  1;
  [5] 1, 1, 4, 12, 37, 60, 80, 63, 33, 10, 1;
  ...

Prog

(PARI) \\ See PARI link in A122078 for program code.
{ my(T=AcyclicDigraphsByArcs(6)); for(n=1, #T, print(T[n])) }

Crossrefs

The labeled version is A081064.

Row sums are A003087.

Cf. A122078, A350449.

Sequence in context: A361012 A363903 A123940 * A339969 A204120 A342666

Adjacent sequences: A350444 A350445 A350446 * A350448 A350449 A350450

Keyword

nonn,tabf

Author

Andrew Howroyd, Dec 31 2021

Status

approved