A357855 - OEIS

A357855

Number of closed trails starting and ending at a fixed vertex in the complete undirected graph on n labeled vertices.

1, 1, 3, 13, 829, 78441, 622316671, 3001764349333, 5926347237626029593

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Trails are directed and pass through each (undirected) edge at most once in either of the two directions.

LINKS

FORMULA

a(n) = Sum_{k = 0..n(n-1)/2} A357885(n,k) = 1 + Sum_{k = 1..n(n-1)/2} A357887(n,k) * k / n.

EXAMPLE

For n = 3, we have a(3) = 3 trails starting and ending at vertex 1: 1 (single vertex), 1->2->3->1, and 1->3->2->1.

CROSSREFS

KEYWORD

nonn,more,walk

AUTHOR

EXTENSIONS

a(9) from Bert Dobbelaere, Oct 17 2022

STATUS

approved