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A365964
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a(n) is n times the minimum moment of inertia of an n-celled polyomino about an axis through the center of mass perpendicular to the plane of the polyomino, with a unit point mass in the center of each of the cells.
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3
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0, 1, 4, 8, 20, 33, 52, 78, 108, 156, 212, 264, 340, 425, 528, 640
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) ~ n^3/(2*Pi).
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EXAMPLE
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For some n, there are more than one polyomino that have the minimum possible moment of inertia. For n = 5, for example, both the P-pentomino and the X-pentomino have the minimum possible moment of inertia a(5)/5 = 4; and for n = 11, the two undecominoes below both have the minimum possible moment of inertia a(11)/11 = 212/11.
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Also for n = 16 there are two polyominoes with the minimum moment of inertia a(16)/16 = 40: the 4 X 4 square and the 5 X 4 square with the corner cells removed. - Pontus von Brömssen, Apr 03 2024
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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