A057572 Number of unlabeled Hugenholtz diagrams with n nodes.

1, 1, 12, 148, 3150, 90075, 3431015, 167013000, 10129020300, 748997001900, 66348135107100, 6937184077639200, 845432117761631400, 118799216331711715800, 19067817942959809023000, 3467025016814436877800000, 708946631468824853456352000, 161976071967463107761759352000

Offset

2,3

Comments

Hugenholtz diagrams are a way of expressing terms in the quantum mechanical many-body perturbation theory.

Hugenholtz diagrams (undirected, as defined by Szabo and Ostlund) are connected 4-regular loopless multigraphs on labeled nodes. - Andrei Zabolotskii, Dec 08 2025

References

A. Szabo and N. Ostlund, Modern Quantum Chemistry, Dover Publications, New York, 1996

Links

Table of n, a(n) for n=2..19.

Sean A. Irvine, Java program (github)

P. D. Stevenson, Automatic Generation of Vacuum Amplitude Many-Body Perturbation Series, Int. J. Mod. Phys. C 14, 1135 (2003).

Crossrefs

Cf. A064732 (directed Hugenholtz diagrams: indegree = outdegree = 2), A367497 (exponential transform, i.e. not necessarily connected), A005816 (loops allowed), A129417 (unlabeled nodes).

Sequence in context: A350655 A167138 A001406 * A114106 A015610 A390389

Adjacent sequences: A057569 A057570 A057571 * A057573 A057574 A057575

Keyword

nonn

Author

Paul Stevenson, Nov 28 2000

Extensions

Offset corrected and a(9)-a(10) from Sean A. Irvine, Jun 17 2022

a(11) onwards from Andrei Zabolotskii, Dec 08 2025

Status

approved