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A353071
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Maximum number of clicks needed to solve any solvable Lights Out problem on an n X n grid.
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0
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1, 4, 9, 7, 15, 36, 49, 64, 37, 100, 65, 144, 169, 123, 225, 124, 199, 324, 197, 400, 441, 484
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OFFSET
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1,2
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COMMENTS
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a(n) = n^2 if and only if A159257(n) = 0.
If n = 6k-1 for some integer k, then a(n) <= 26k^2 - 12k + 1. This upper bound is equal to a(n) when A159257(n) = 2. Further, it is conjectured that if A159257(n) = 2, then n = 6k-1 for some integer k.
It is conjectured that if A159257(n) = 4, then n = 5k-1 for some integer k, and a(n) = 17k^2 - 10k.
It is conjectured that if A159257(n) = 6, then n = 12k-1 for some integer k, and a(n) = 88k^2 - 24k + 1
It is conjectured that if A159257(n) = 8, then either n = 10k-1 or n = 17k-1 for some integer k. If n = 10k-1, then a(n) = 60k^2 - 20k - 3. If n = 17k-1, then a(n) = 161k^2 - 34k - 3.
It is conjectured that if A159257(n) = 10, then n = 30k-1 for some integer k, and a(n) = 506k^2 - 60k - 3.
239 <= a(23) <= 305.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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