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A329094
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a(n) is the number of solutions when placing the numbers 1..n in an n X n square according to the rules in the Comments section.
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0
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1, 1, 1, 1, 1, 3, 3, 8, 17, 18, 51, 69, 126, 286, 485, 1180, 2245, 4312, 7247, 19559, 41403, 66454, 161131, 337495, 710899, 1286527, 3069554, 7100614, 15046664, 29090692, 57797782, 144576706, 313441617, 628544270, 1278592587, 3304149943, 7192582862
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OFFSET
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1,6
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COMMENTS
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Place a 1 in the upper left corner of the square. Let k be the number placed last. At each step place k+1 at a distance k vertically or horizontally from k. Solutions are counted up to mirroring in the backward diagonal. That is, all solutions have 2 to the right of 1. Obviously, n is the largest possible value since the next step will inevitably lead outside the square.
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LINKS
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EXAMPLE
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Sample solutions:
n=6 n=7 n=8
1 2 - - - - 1 2 - - - - - 1 2 - - - - 8 -
- - - - - - 7 5 - - - - 6 - - - - - - - -
- 3 - - - - - 3 - - - - - 5 3 - - 4 - - -
- - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - -
6 4 - - - 5 - 4 - - - - - - - - - - - - -
- - - - - - - - - - - - - - -
6 - - - - - 7 -
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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