Search: id:A086441
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%I A086441
%S A086441 1,1,2,4,11,27,79,213,644,1840,5660
%N A086441 Number of inequivalent ways a semi-infinite curve can cross a straight 
               line n times.
%C A086441 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 A086441 <a href="Sindx_Fo.html#fold">Index entries for sequences obtained by 
               enumerating foldings</a>
%e A086441 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 A086441 ......--........X
%e A086441 ...../..\....../
%e A086441 ----*----*----*----
%e A086441 .../......\../
%e A086441 ../........--
%e A086441 ./
%e A086441 oo
%e A086441 ........---
%e A086441 ......./...\
%e A086441 ....../..X..\
%e A086441 ...../...|...\
%e A086441 ----*----*----*----
%e A086441 .../.....|.../
%e A086441 ../.......---
%e A086441 ./
%e A086441 oo
%Y A086441 Isomorphism classes (using too generous a definition of isomorphism) 
               from A000682. Cf. A000560, A001011.
%Y A086441 Sequence in context: A123440 A071314 A123441 this_sequence A148130 A131482 
               A148131
%Y A086441 Adjacent sequences: A086438 A086439 A086440 this_sequence A086442 A086443 
               A086444
%K A086441 nonn,more
%O A086441 1,3
%A A086441 N. J. A. Sloane (njas(AT)research.att.com), Sep 09 2003

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