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Search: id:A123690
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| A123690 |
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Number of points in a square lattice covered by a circle of diameter n if the center of the circle is chosen such that the circle covers the maximum possible number of lattice points. |
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+0
4
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| 2, 5, 9, 14, 22, 32, 41, 52, 69, 81, 97, 116, 137, 157, 180, 208, 231, 258, 293, 319
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n)>=max(A053411(n),A053414(n),A053415(n)).
a(n) is an upper bound for the number of segments of a self avoiding path on the 2-dimensional square lattice such that the path fits into a circle of diameter n. A122224(n)<=a(n). Link to illustrations added. X-Refs to A125852 and A127406.
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LINKS
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Hugo Pfoertner, Maximum number of points in the square lattice covered by circular disks. Illustrations.
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EXAMPLE
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a(1)=2: Circle with diameter 1 and center (0,0.5) covers 2 lattice points; a(2)=5: Circle with diameter 2 and center (0,0) covers 5 lattice points;
a(3)=4: Circle with diameter 3 and center (0,0) covers 9 lattice points;
a(4)=14: Circle with diameter 4 and center (0.5,0.2) covers 14 lattice points.
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CROSSREFS
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Cf. A123689, A053411, A053414, A053415, A122224.
The corresponding sequences for the hexagonal lattice and the honeycomb net are A125852 and A127406, respectively.
Sequence in context: A026053 A011905 A098065 this_sequence A090937 A071609 A068501
Adjacent sequences: A123687 A123688 A123689 this_sequence A123691 A123692 A123693
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KEYWORD
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more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 09 2006, Feb 11 2007
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