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

1,2

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

Table of n, a(n) for n=1..21.

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.

Formula

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

Crossrefs

Diagonal sums of A360862.

Sequence in context: A089468 A109498 A142967 * A201339 A370877 A254789

Adjacent sequences: A360861 A360862 A360863 * A360865 A360866 A360867

Keyword

nonn

Author

Andrew Howroyd and William P. Orrick, Feb 24 2023

Status

approved