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A086441 Number of inequivalent ways a semi-infinite curve can cross a straight line n times. 2
1, 1, 2, 4, 11, 27, 79, 213, 644, 1840, 5660 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 14 15:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)