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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.
0
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
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
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jan 13 2019
EXTENSIONS
Terms a(6) and beyond from Andrew Howroyd, May 05 2023
STATUS
approved