|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|