A008987 -id:A008987 - cp's OEIS frontend

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.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Mar 02 2016

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.

Cf. A008986, A008987, A268564, A373325.

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

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

A268564 Number of immersions of unoriented circle into oriented sphere with 2n double points such that two different choices of orientation of the circle are not related by geotopy.

Original entry on oeis.org

0, 1, 16, 555, 27155, 1624602, 110848296, 8306916404, 667683029392

Offset: 0

N. J. A. Sloane, Mar 02 2016

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), s_s.

Cf. A008986, A008987, A268563.

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

Name clarified and a(0), a(6)-a(8) added using formula by Andrey Zabolotskiy, Jun 08 2024

A268565 Number of achiral immersions of oriented circle into oriented sphere with 2n double points.

Original entry on oeis.org

1, 1, 5, 15, 97, 592, 4488, 35314, 295379

Offset: 0

N. J. A. Sloane, Mar 03 2016

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. (17), r_m.

Cf. A008986, A008987, A268566.

a(n) = 2 * A008988(2*n) - A008986(2*n). - Andrey Zabolotskiy, Jun 05 2024

Name clarified and a(0), a(6)-a(8) added using formula by Andrey Zabolotskiy, Jun 08 2024

A268566 Number of chiral immersions of oriented circle into oriented sphere with 2n double points.

Original entry on oeis.org

0, 1, 16, 564, 27231, 1625324, 110854838, 8306977585, 667683610221

Offset: 0

N. J. A. Sloane, Mar 03 2016

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. (17), s_m.

Cf. A008986, A008987, A268565.

a(n) = A008986(2*n) - A008988(2*n). - Andrey Zabolotskiy, Jun 05 2024

Name clarified and a(0), a(6)-a(8) added using formula by Andrey Zabolotskiy, Jun 08 2024

cp's OEIS Frontend

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.

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A268564 Number of immersions of unoriented circle into oriented sphere with 2n double points such that two different choices of orientation of the circle are not related by geotopy.

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A268565 Number of achiral immersions of oriented circle into oriented sphere with 2n double points.

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A268566 Number of chiral immersions of oriented circle into oriented sphere with 2n double points.

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