A268572
Number of bicolored immersions of unoriented circle into oriented sphere with n double points and no simple loop.
Original entry on oeis.org
0, 0, 2, 1, 4, 9, 38, 133, 640, 2864
Offset: 1
A268559
Number of bicolored immersions of unoriented circle into oriented surface with n double points, up to stable geotopy.
Original entry on oeis.org
2, 3, 14, 54, 420, 3886, 46470, 645524, 10328214
Offset: 1
- Robert Coquereaux and Jean-Bernard Zuber, Maps, immersions and permutations, Journal of Knot Theory and Its Ramifications, Vol. 25, No. 8 (2016), 1650047; arXiv preprint, arXiv:1507.03163 [math.CO], 2015-2016. See Table 9, line UOc total.
A268573
Number of irreducible indecomposable bicolored immersions of unoriented circle into oriented sphere with n double points.
Original entry on oeis.org
0, 0, 2, 1, 4, 6, 24, 73, 322, 1274
Offset: 1
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).
Original entry on oeis.org
2, 16, 336, 12480, 689664, 51440640, 4870932480, 561752432640, 76597275525120, 12077498082263040, 2164587437201817600, 434984457687426662400, 96927605985557820211200, 23730144990202925206732800, 6333914501366616792288460800, 1831049666989439061980086272000
Offset: 1
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