A268573 Number of irreducible indecomposable bicolored immersions of unoriented circle into oriented sphere with n double points.

0, 0, 2, 1, 4, 6, 24, 73, 322, 1274, 5986, 27750, 135890, 676263, 3441088, 17811771, 93550146, 497835030, 2680159902, 14577839412, 80039631744, 443164758244, 247271664934

Offset

1,3

Links

Table of n, a(n) for n=1..23.

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 7.

Formula

a(2*n) = A264761(2*n), a(2*n+1) = 2 * A264760(2*n+1). - Andrei Zabolotskii, Jun 05 2024

Crossrefs

Cf. A264760, A264761, A268561, A268572.

Sequence in context: A367716 A019142 A330536 * A145858 A328491 A328357

Adjacent sequences: A268570 A268571 A268572 * A268574 A268575 A268576

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 03 2016

Extensions

Name clarified by Andrei Zabolotskii, Jun 08 2024

a(11)-a(23) from Andrei Zabolotskii, Dec 28 2025

Status

approved