A268563 Number of immersions of unoriented circle into oriented sphere with 2n double points such that two different choices of orientation of the circle are related by geotopy.

1, 1, 5, 33, 249, 2036, 17572, 157676, 1457037

Offset

0,3

Links

Table of n, a(n) for n=0..8.

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 Eq. (16), r_s.

Formula

a(n) = 2 * A008987(2*n) - A008986(2*n). - Andrey Zabolotskiy, Jun 05 2024

Crossrefs

Cf. A008986, A008987, A268564, A373325.

Sequence in context: A153398 A242522 A034015 * A056159 A364792 A367280

Adjacent sequences: A268560 A268561 A268562 * A268564 A268565 A268566

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 02 2016

Extensions

Name clarified and a(0), a(6)-a(8) added using formula by Andrey Zabolotskiy, Jun 07 2024

Status

approved