A127910 -id:A127910 - cp's OEIS frontend

A127909 Number of different digraphs on n unlabeled nodes which are not graphs.

0, 0, 1, 12, 207, 9574, 1540788, 882032396, 1793359180502, 13027956824124884, 341260431952960575184, 32522909385055885092199576, 11366745430825400574268802831632, 14669085692712929869037045573284852976, 70315656615234999521385506526925748433982432

Offset: 0

Jonathan Vos Post, Feb 06 2007

A digraph is (isomorphic to) a graph if every pair of points a, b joined by a directed edge (a,b) also has the reverse directed edge (b,a). A digraph which is not a graph is a digraph with at least one pair of points which have only one directed edge connecting them.

			a(2) = 1 because with two points a and b, either there are no edges connecting them, or there is one directed edge between them, or there is a bidirectional pair of edges between them; only the case with one directed edge is the unique 2-point digraph which is not a graph.

Chai Wah Wu, Table of n, a(n) for n = 0..60

Cf. A000088, A000273, A127910-A127915.

from itertools import combinations
from math import prod, factorial, gcd
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A127909(n): return int(sum(Fraction((1<>1)*r+(q*r*(r-1)>>1) for q, r in p.items())),prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n))) # Chai Wah Wu, Jul 05 2024

a(n) = A000273(n) - A000088(n).

cp's OEIS Frontend

A127909 Number of different digraphs on n unlabeled nodes which are not graphs.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Formula