A360864 Number of unlabeled connected multigraphs with circuit rank n and degree >= 3 at each node, loops allowed.

0, 3, 15, 111, 1076, 13870, 220520, 4185406, 92235118, 2314204852, 65129484278, 2032179006943, 69640160993587, 2600585852722150, 105127528809344785, 4574251821427917425, 213171992131468465801, 10593983324971249199532, 559293301762878627195807, 31259896932477899016109585, 1844062168535890557437809526

Offset: 1

Author

Andrew Howroyd and William P. Orrick, Feb 24 2023

Keywords

• nonn

Comments

The terms up to a(21) were computed by Michael Borinsky and Jos Vermaseren using a program written in FORM. The graphs enumerated by a(n) are called admissible (Borinsky and Vogtmann, 2023).

Links

• Michael Borinsky and Karen Vogtmann, The Euler characteristic of the moduli space of graphs, arXiv:2301.01121 [math.AT], 2023.
• Tony Guttmann, Asymptotics for A360864
• Leila Sloman, Quantum Field Theory Pries Open Mathematical Puzzle, Quanta Magazine, Feb 2023.

Crossrefs

Diagonal sums of A360862.

Formula

a(n) = Sum_{k>=1} A360862(n + k - 1, k).