A268560 Number of bicolored maps defined by immersions of unoriented circle into oriented sphere with n double points with edges labeled 1..2*n such that labels of successive edges along the curve (starting at any edge, going in the direction determined by the coloring) are encountered in pairs of the form {2*m-1, 2*m} (in either order).

2, 16, 336, 12480, 689664, 51440640, 4870932480, 561752432640, 76597275525120, 12077498082263040, 2164587437201817600, 434984457687426662400, 96927605985557820211200, 23730144990202925206732800, 6333914501366616792288460800, 1831049666989439061980086272000

Offset

1,1

Links

Table of n, a(n) for n=1..16.

R. Coquereaux and J.-B. Zuber, Maps, immersions and permutations, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: 10.1142/S0218216516500474.

Formula

a(n) = A268567(n) * 2^n [proof: labeling the vertex incident to a pair {2*m-1, 2*m} by m defines a 2^n-to-one map from edge-labeled curves to vertex-labeled curves; and a bijection between vertex-labeled bicolored unoriented immersions and vertex-labeled (uncolored) oriented immersions can be defined e.g. by requiring that the pair of edges going from vertex #1 is incident to a shaded region]. - Andrey Zabolotskiy, Jan 14 2025

Crossrefs

Cf. A268567, A268561.

Sequence in context: A294039 A009100 A009109 * A275854 A299907 A012610

Adjacent sequences: A268557 A268558 A268559 * A268561 A268562 A268563

Keyword

nonn

Author

N. J. A. Sloane, Mar 02 2016

Extensions

New name and terms a(11) onwards from Andrey Zabolotskiy, Jan 21 2025

Status

approved