A086441 Number of inequivalent ways a semi-infinite curve can cross a straight line n times.

1, 1, 2, 4, 11, 27, 79, 213, 644, 1840, 5660

Offset

1,3

Comments

This uses a too broad notion of equivalence. Besides the obvious reflection in a plane perpendicular to the straight line, if the end of the curve is in a free region of the plane, it is extended to infinity and the direction of the curve can then be reversed. A000560 uses a better definition of equivalence.

Links

Table of n, a(n) for n=1..11.

Index entries for sequences obtained by enumerating foldings

Example

The a(3) = 2 solutions with 3 crossings. The line is drawn horizontally. The curve starts at oo and ends at X. The crossings are indicated by stars.
       --        X
      /  \      /
-----*----*----*----
    /      \  /
   /        --
  /
oo
         ---
        /   \
       /  X  \
      /   |   \
-----*----*----*----
    /     |   /
   /      .---
  /
oo

Crossrefs

Isomorphism classes (using too generous a definition of isomorphism) from A000682. Cf. A000560, A001011.

Sequence in context: A071314 A309886 A123441 * A316696 A319616 A148130

Adjacent sequences: A086438 A086439 A086440 * A086442 A086443 A086444

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 09 2003

Status

approved