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A343540
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Squares visited by a trapped knight on a square-spiral numbered board where the knight is shifted one square up and one square to the right after each move.
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0
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1, 10, 7, 6, 5, 4, 3, 12, 13, 8, 9, 44, 45, 42, 41, 40, 39, 18, 17, 16, 15, 14, 11, 26, 27, 28, 29, 30, 31, 34, 33, 32, 35, 62, 61, 38, 37, 64, 63, 98, 97, 96, 95, 94, 93, 56, 53, 50, 47, 114, 73, 154, 109, 108, 107, 106, 105, 104, 103, 102
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OFFSET
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1,2
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COMMENTS
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The squares are numbered starting with 1 at the origin (0,0). The sequence is finite: when arriving on square number a(180) = 157, there is no free square within reach for the next move.
Shifting the knight only 1 square to the right leads to an infinite sequence. Similarly, shifting only 1 square up leads to an infinite sequence. More generally, if the knight jumps (1,n) spaces and is shifted m squares to the right, m > n leads to an infinite sequence.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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