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A125852
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Number of points in a hexagonal lattice covered by a circular disk of diameter n if the center of the circle is chosen such that the disk covers the maximum possible number of lattice points.
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9
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2, 7, 10, 19, 24, 37, 48, 61, 77, 94, 115, 134, 157, 187, 208, 241, 265, 301, 330, 367, 406, 444, 486, 527, 572, 617, 665, 721, 769, 825, 877, 935, 993, 1054, 1117, 1182, 1249, 1316, 1385, 1459, 1531, 1615, 1684, 1765, 1842, 1925, 2011, 2096, 2187, 2276
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)>=max(A053416(n),A053479(n),A053417(n)). a(n) is an upper bound for the number of segments of a self avoiding path on the 2-dimensional triangular lattice such that the path fits into a circle of diameter n. A122226(n)<=a(n).
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LINKS
| H. v. Eitzen, Table of n, a(n) for n=1..1000
Index entries for sequences related to A2 = hexagonal = triangular lattice
Hugo Pfoertner, Maximum number of points in the hexagonal lattice covered by circular disks. Illustrations.
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CROSSREFS
| Cf. A053416, A053479, A053417, A125851, A122226. The corresponding sequences for the square lattice and the honeycomb net are A123690 and A127406, respectively.
Sequence in context: A059316 A105770 A152211 * A155171 A049830 A022302
Adjacent sequences: A125849 A125850 A125851 * A125853 A125854 A125855
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 07 2007, Feb 11 2007
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EXTENSIONS
| More terms copied from b-file by Hagen von Eitzen (math(AT)von-eitzen.de), Jun 17 2009
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