A329426 Number of non-isomorphic directed graphs where every vertex has outdegree 1, and no self-loops.

1, 2, 6, 20, 97, 550, 3794, 29826, 266527, 2649156, 29040865, 347548542, 4509961264, 63050417976, 944767674590, 15103712944100, 256594870255076, 4616238126871328, 87670085904641440, 1752759735606185804, 36796608121601906104, 809312755145598475440, 18609995953274373396982

Offset

2,2

Links

Stephen Dunn, Table of n, a(n) for n = 2..100

Formula

a(n) = 1 + A329427(n) + A056542(n-1).

a(n) = 1 + A056542(n-1) + Sum_{2..floor(n/2)} a(i)*a(n-i).

Example

For n = 2, a(2) = 1 + A329427(2) + A056542(1) = 1 + 0 + 0 = 1, which is the graph A <--> B.
For n = 3, a(3) = 1 + A329427(3) + A056542(2) = 1 + 0 + 1 = 2, which are graphs A --> B <--> C and A --> B --> C --> A.
The middle term is nonzero when there are graphs with more than 1 component.

Prog

(Kotlin)
fun A329427(n: Long): Long = (2L..(n/2)).map { a(it) * a(n-it) }.sum()
fun A056542(n: Long): Long = if (n == 1L) 0 else n * A056542(n-1) + 1
fun a(n: Long): Long = 1 + A329427(n) + A056542(n-1)

Crossrefs

Cf. A329427, A056542.

Sequence in context: A079570 A131842 A348104 * A020095 A026991 A049379

Adjacent sequences: A329423 A329424 A329425 * A329427 A329428 A329429

Keyword

nonn

Author

Stephen Dunn, Nov 30 2019

Status

approved