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Number of inequivalent ways a semi-infinite curve can cross a straight line n times.
2

%I #9 Apr 16 2021 00:13:51

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

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

%C 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.

%H <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>

%e 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.

%e -- X

%e / \ /

%e -----*----*----*----

%e / \ /

%e / --

%e /

%e oo

%e ---

%e / \

%e / X \

%e / | \

%e -----*----*----*----

%e / | /

%e / .---

%e /

%e oo

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

%K nonn,more

%O 1,3

%A _N. J. A. Sloane_, Sep 09 2003