A350492 -id:A350492 - cp's OEIS frontend

A345258 Number of acyclic digraphs (or DAGs) on n unlabeled vertices with one source and one sink.

1, 1, 2, 10, 98, 1960, 80176, 6686760, 1129588960, 384610774696, 263104175114712, 360908867732030980, 991603865814038728388, 5453395569997436383751204, 60010050181461052836515513108, 1321051495313052133670927704328040, 58170762510305449187073353930875222256

Offset: 1

Max Alekseyev, Jun 12 2021

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..50 (terms 1..40 from Mikhail Tikhomirov)
Marcel et al., Is there a formula for the number of st-dags (DAG with 1 source and 1 sink) with n vertices?, MathOverflow, 2021.

Row sums of A350491.
The labeled version is A165950.
Cf. A003087, A049531, A122078, A350415, A350492.

A345258seq(16) \\ See PARI link in A122078 for program code.

a(9) from Brendan McKay.

Terms a(10) and beyond from Mikhail Tikhomirov, Jun 16 2021

A350491 Triangle read by rows: T(n,k) is the number of acyclic digraphs on n unlabeled nodes with k arcs and a global source and sink, n >= 1, k = 0..n*(n-1)/2.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 1, 9, 25, 32, 22, 8, 1, 0, 0, 0, 0, 0, 1, 17, 92, 259, 441, 496, 379, 195, 66, 13, 1, 0, 0, 0, 0, 0, 0, 1, 28, 259, 1286, 4026, 8754, 13930, 16686, 15289, 10785, 5842, 2397, 722, 151, 19, 1

Offset: 1

Andrew Howroyd, Jan 08 2022

			Triangle begins:
  [1] 1;
  [2] 0, 1;
  [3] 0, 0, 1, 1;
  [4] 0, 0, 0, 1, 4, 4,  1;
  [5] 0, 0, 0, 0, 1, 9, 25, 32,  22,   8,   1;
  [6] 0, 0, 0, 0, 0, 1, 17, 92, 259, 441, 496, 379, 195, 66, 13, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..1350 (rows 1..20)

Row sums are A345258.
Column sums are A350492.
Cf. A122078, A350447, A350449, A350488.

\\ See PARI link in A122078 for program code.
{ my(A=A350491rows(7)); for(i=1, #A, print(A[i])) }

A350490 Number of unlabeled acyclic digraphs with n arcs and a global source.

Original entry on oeis.org

1, 1, 2, 5, 15, 50, 191, 795, 3625, 17781, 93319, 519732, 3056185, 18880345, 122066437, 823118881, 5772473719, 41995743085, 316258151517, 2460542117337, 19743544526463, 163138014893817, 1386173917051704, 12096681529032989, 108293699332498981

Offset: 0

Andrew Howroyd, Jan 08 2022

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..40

Column sums of A350488.

Cf. A122078, A350415, A350451, A350492.

A350490seq(20) \\ See PARI link in A122078 for program code.

cp's OEIS Frontend

A345258 Number of acyclic digraphs (or DAGs) on n unlabeled vertices with one source and one sink.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Extensions

A350491 Triangle read by rows: T(n,k) is the number of acyclic digraphs on n unlabeled nodes with k arcs and a global source and sink, n >= 1, k = 0..n*(n-1)/2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

A350490 Number of unlabeled acyclic digraphs with n arcs and a global source.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI