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%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