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A231255
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a(n) is the smallest integer t such that every length-t walk from the origin (0,0) taking steps of either (0,1) or (1,0) is guaranteed to have n points that are collinear.
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0
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OFFSET
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1,3
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COMMENTS
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By length-t we mean the number of steps, one less than the number of points.
It is known that a(7) >= 261.
Longest sequences avoiding n collinear points, encoded by 1 for (0,1) and 2 for (1,0):
n = 3: 121
n = 4: 11211211
n = 5: 1121112111211122212221222122
n = 6: 112111222212222122221211211112112122221222212222122221211211112111221222212222122221221112111221
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LINKS
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EXAMPLE
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a(3) = 4 because two consecutive identical steps from (0,0) generate 3 collinear points, so the first three steps must be (0,1), (1,0), (0,1) or its complement. Then no matter what is chosen for the next step, three collinear points are generated.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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