A265580 Number of (unlabeled) loopless multigraphs with no isolated vertices such that the sum of the numbers of vertices and edges is n.

1, 0, 0, 1, 1, 2, 4, 7, 13, 27, 54, 112, 243, 538, 1223, 2875, 6909, 17052, 43138, 111686, 295658, 799684, 2207356, 6213391, 17820961, 52042771, 154640528, 467254731, 1434837672, 4475520062, 14173115724, 45548395180, 148485883443, 490831193397, 1644581336531

Offset: 0

Author

Michael Joseph, Dec 10 2015

Keywords

• nonn

Comments

Also the number of skeletal 2-cliquish graphs with n vertices and no isolated vertices. See Einstein et al. link below.

Examples

			For n = 5, the a(5) = 2 such multigraphs are the graph with three vertices and edges from one vertex to each of the other two, and the graph with two vertices connected by three edges.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100
• D. Einstein, M. Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp and S. Rubinstein-Salzedo, Noncrossing partitions, toggles, and homomesies, arXiv:1510.06362 [math.CO], 2015.

Crossrefs

Cf. A265581.

Formula

a(n) = A265581(n) - A265581(n-1), n>=1.

Extensions

Terms a(19) and beyond from Andrew Howroyd, Feb 01 2020