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

0,6

Comments

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

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.

Formula

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

Example

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.

Crossrefs

Cf. A265581.

Sequence in context: A256942 A112740 A309050 * A136408 A317718 A357931

Adjacent sequences: A265577 A265578 A265579 * A265581 A265582 A265583

Keyword

nonn

Author

Michael Joseph, Dec 10 2015

Extensions

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

Status

approved