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Search: id:A086441
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| A086441 |
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Number of inequivalent ways a semi-infinite curve can cross a straight line n times. |
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+0
3
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| 1, 1, 2, 4, 11, 27, 79, 213, 644, 1840, 5660
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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.
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LINKS
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Index entries for sequences obtained by enumerating foldings
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EXAMPLE
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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
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CROSSREFS
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Isomorphism classes (using too generous a definition of isomorphism) from A000682. Cf. A000560, A001011.
Sequence in context: A123440 A071314 A123441 this_sequence A148130 A131482 A148131
Adjacent sequences: A086438 A086439 A086440 this_sequence A086442 A086443 A086444
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KEYWORD
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nonn,more
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AUTHOR
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njas, Sep 09 2003
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