A069831 Number of graphical partitions of simple Eulerian graphs (partitions given by the degrees of vertices of simple (no loops or multiple edges) graphs having only vertices of even degrees) having n edges.

1, 0, 0, 1, 1, 1, 2, 3, 3, 5, 8, 10, 13, 16, 22, 29, 36, 45, 61, 74, 95, 118, 152, 183, 232, 279, 354, 422, 524, 627, 780, 926, 1134, 1355, 1651, 1958, 2366, 2809, 3372, 3988, 4757, 5628, 6678, 7874, 9283, 10964, 12861, 15130, 17686, 20799, 24209, 28389

Offset: 0

Author

Roland Bacher, Apr 23 2002

Keywords

• nonn

Examples

			a(1)=a(2)=0 since Eulerian graphs having 1 or 2 edges are not simple. The triangle is the unique Eulerian graph having 3 edges and no isolated vertices, thus showing a(3)=1.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..100
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A000569.