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A361135 The number of unlabeled connected fairly 4-regular multigraphs of order n, loops allowed. 5
1, 3, 8, 30, 118, 548, 2790, 16029, 101353, 706572, 5375249, 44402094, 395734706, 3786401086, 38711834576, 421217184135, 4860174299186, 59278045511959, 762055884150141, 10299293881159294, 145994591873294780, 2165938721141964179, 33564939201581495090, 542344644703485899950, 9122110321170144880053 (list; graph; refs; listen; history; text; internal format)
Edges are undirected, vertices not labeled. "Fairly" means that each vertex has degree 4, but two of these edges do not connect to a second vertex; they are "fins" in CAD speak or "half-edges" in perturbation theory. The two fins may be attached to the same or to two different nodes. In the usual mathematical nomenclature these are connected graphs of order n+2 with two vertices of degree 1 and n vertices of degree 4, loops allowed.
H. Kleinert, A. Pelster, B. Kastening, and M. Bachmann, Recursive graphical construction of Feynman diagrams and their multiplicities in Phi^4 and Phi^2*A theory, Phys. Rev. E 62 (2) (2000), 1537 Table II.
R. J. Mathar, Illustrations
Cf. A085549 (4-regular), A352174 (assuming rooted external legs).
Sequence in context: A151440 A213860 A360991 * A348662 A162560 A293250
R. J. Mathar, Mar 02 2023
Terms a(7) and beyond from Andrew Howroyd, Mar 05 2023

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