A008985 Triangle T(n,k) giving number of immersions of the oriented circle into the oriented plane with n double points and index k, k = -n-1, -n+1, ..., n-1, n+1.

0, 1, 1, 1, 1, 1, 2, 3, 3, 2, 4, 10, 11, 10, 4, 10, 35, 57, 57, 35, 10, 26, 133, 290, 364, 290, 133, 26

Offset

-1,7

References

V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 18.

Links

Table of n, a(n) for n=-1..26.

S. V. Duzhin, Computer programs and data files of the participants of Arnold's seminar, 1998-2010.

S. M. Gusein-Zade and F. S. Duzhin, On the number of topological types of plane curves; (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197-198. English translation: Russian Mathematical Surveys 53 (1998) 626-627.

Formula

T(n, n+1) = A003239(n). [Arnold, p. 12] - Andrey Zabolotskiy, Oct 22 2023

Crossrefs

Cf. A008980 (row sums), A008981, A008982, A008983, A054993, A008984 (k = n-1), A003239 (k = n+1).

Sequence in context: A073078 A360296 A034799 * A326699 A138652 A323833

Adjacent sequences: A008982 A008983 A008984 * A008986 A008987 A008988

Keyword

nonn,nice,tabl,more

Author

N. J. A. Sloane

Extensions

Name clarified and initial row added by Andrey Zabolotskiy, Oct 22 2023

Status

approved