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A163437
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Number of different fixed (possibly) disconnected polyominoes (of any area) bounded tightly by an n X n square.
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5
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1, 7, 322, 51472, 29671936, 64588152832, 545697103347712, 18161310923858378752, 2399054119350722118025216, 1262710910458264839283982467072, 2653270028014955753823799266500411392
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2^(n^2) - 4*2^((n-1)*n) + 4*2^((n-1)^2) + 2*2^((n-2)*n) - 4*2^((n-2)*(n-1)) + 2^((n-2)^2).
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EXAMPLE
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a(2)=7: 2 rotations of the strictly disconnected domino consisting of two squares connected at a vertex, 4 rotations of the L tromino, and the square tetromino.
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MATHEMATICA
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Table[2^(n^2) - 4*2^((n - 1)*n) + 4*2^((n - 1)^2) + 2*2^((n - 2)*n) -
4*2^((n - 2)*(n - 1)) + 2^((n - 2)^2), {n, 1, 25}] (* G. C. Greubel, Dec 23 2016 *)
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CROSSREFS
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Cf. A162677 (bound not necessarily tight), A163433 (fixed disconnected trominoes), A163434 (fixed disconnected tetrominoes), A163435 (fixed disconnected pentominoes), A163436 (fixed disconnected n-ominoes).
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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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