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A141225
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Number of points having maximal visibility in a square n x n lattice.
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5
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1, 4, 1, 4, 8, 16, 8, 12, 16, 36, 9, 60, 16, 16, 8, 12, 12, 12, 12, 36, 16, 16, 25, 4, 16, 8, 5, 12, 24, 64, 12, 8, 4, 4, 25, 16, 4, 8, 1, 20, 16, 4, 20, 12, 4, 4, 9, 8, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 9, 4, 8, 4, 8, 12, 8, 4, 4, 8, 4, 16, 12, 20, 4, 8, 4, 4, 16, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sequence A141224 gives the maximum number of points visible from some point. By symmetry, when a(n) is odd, the central point in the lattice can see the maximal number of points. When a(n)=1, the central point is the only such point. See A141226 for the n x n lattices that have such a central point.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
| Table[mx=0; pts=0; Do[cnt=0; Do[If[GCD[c-a, d-b]<2, cnt++ ], {a, n}, {b, n}]; If[cnt>mx, mx=cnt; pts=1, If[cnt==mx, pts++ ]], {c, n}, {d, n}]; pts, {n, 20}]
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CROSSREFS
| Sequence in context: A072812 A162956 A131112 * A079185 A133819 A021245
Adjacent sequences: A141222 A141223 A141224 * A141226 A141227 A141228
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jun 15 2008
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