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A329427 Number of directed graphs of n vertices with more than 1 component and out degree = 1. 3
1, 2, 10, 32, 173, 864, 5876, 42654, 369352, 3490396, 37205377, 431835570, 5488938513, 75253166882, 1111054042385, 17529435042906, 294620759901439, 5250432711385802, 98912760811106081, 1963457208200874954, 40962100714228585825, 895889161265034629994, 2049759384024221189190 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

a(n) gives the number of unique ways a directed graph of n vertices with out degree 1 can be broken into smaller components of size >= 2. It can be generalized to higher degree by replacing A329426 in the formula with a suitable counting function.

LINKS

Stephen Dunn, Table of n, a(n) for n = 4..100

FORMULA

a(n) = Sum_{i=2..floor(n/2)} A329426(i) * A329426(n-i).

EXAMPLE

a(4) = A329426(2)*A329426(2) = 1*1 = 1, which represents the graph

V <--> V

V <--> V.

a(5) = A329426(2)*A329426(3) = 1*2 = 2, which represents the two possible graphs of size 3 (V --> V <--> V, etc.) paired with V <--> V.

a(6) = A329426(2)*A329426(4) + A329426(3)*A329426(3) = 1*6 + 2*2 = 10.

PROG

(Kotlin)

fun A056542(n: Long): Long = if (n == 1L) 0 else n * A056542(n-1) + 1

fun A329426(n: Long): Long = 1 + a(n) + A056542(n-1)

fun a(n: Long): Long = (2L..(n/2)).map { A329426(it) * A329426(n-it) }.sum()

CROSSREFS

Cf. A329426, A056542.

Sequence in context: A328039 A264960 A151019 * A004028 A263839 A236921

Adjacent sequences:  A329424 A329425 A329426 * A329428 A329429 A329430

KEYWORD

nonn

AUTHOR

Stephen Dunn, Nov 30 2019

STATUS

approved

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Last modified April 13 11:56 EDT 2021. Contains 342936 sequences. (Running on oeis4.)