A323389 The number of connected, unlabeled, undirected, edge-signed cubic graphs (admitting loops and multiedges) on 2n vertices where the degree of the first sign is 2 at each node.

1, 2, 5, 19, 88, 553, 4619, 49137, 646815, 10053183, 178725865, 3555840644, 78048875298, 1871066903575, 48617053973267, 1360733669185473, 40810827325698897, 1305690378666580997, 44387116312631271929, 1597768080980647428027, 60710507893875818581964

Offset

0,2

Comments

Obtained from the cubic graphs A005967 (connected undirected cubic graphs that may have loops and/or multiedges) by signing each edge with a plus or a minus such that two pluses and one minus meet at each vertex.

Links

Table of n, a(n) for n=0..20.

Richard J. Mathar, Feynman diagrams of the QED vacuum polarization, vixra:1901.0148 (2019) Section II.

Prog

(PARI) \\ See A339645 for combinatorial species functions.
cycleIndexSeries(n)={1+sLog(sCartProd(sExp(dihedralGroupSeries(n)), sExp(symGroupCycleIndex(2)*x^2 + O(x*x^n))))}
seq(n)={Vec(substpol(OgfSeries(cycleIndexSeries(2*n)), x^2, x))} \\ Andrew Howroyd, May 05 2023

Crossrefs

Cf. A005967 (unsigned), A054499 (only one cycle of pluses), A170946 (directed plus-edges).

Sequence in context: A326563 A316700 A124348 * A268605 A205804 A052324

Adjacent sequences: A323386 A323387 A323388 * A323390 A323391 A323392

Keyword

nonn

Author

R. J. Mathar, Jan 13 2019

Extensions

Terms a(6) and beyond from Andrew Howroyd, May 05 2023

Status

approved