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A335573
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a(n) is the number of fixed polyominoes corresponding to the free polyomino represented by A246521(n).
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18
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1, 1, 2, 4, 2, 8, 1, 4, 4, 2, 8, 4, 4, 8, 8, 8, 4, 4, 8, 4, 1, 2, 4, 8, 8, 8, 2, 8, 8, 8, 8, 8, 4, 8, 4, 8, 8, 8, 8, 4, 4, 8, 4, 8, 8, 8, 4, 4, 4, 4, 8, 8, 4, 8, 4, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 8, 2, 8, 8, 8, 8, 8, 4, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8
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OFFSET
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1,3
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COMMENTS
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Each free polyomino represented by a number in A246521 may correspond to 1, 2, 4 or 8 different fixed polyominoes, generated by rotation or reflection.
In the sequence A246521, the size n polyominoes start at position j = 1 + Sum_{i=0..n-1} A000105(i) and end at position k = Sum_{i=0..n} A000105(i). Therefore, the number of fixed polyominoes, A001168(n), is equal to Sum_{i=j..k} a(i).
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LINKS
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EXAMPLE
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The size 4 L-shaped polyomino represented by A246521(6) will generate 8 fixed polyominoes.
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CROSSREFS
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Cf. A000105 (number of free polyominoes of size n).
Cf. A001168 (number of fixed polyominoes of size n).
Cf. A246521 (list of free polyominoes in binary coding).
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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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