A141225 Number of points having maximal visibility in a square n x n lattice.

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

Offset

1,2

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.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

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}]

Crossrefs

Sequence in context: A244097 A162956 A131112 * A344947 A079185 A133819

Adjacent sequences: A141222 A141223 A141224 * A141226 A141227 A141228

Keyword

nonn

Author

T. D. Noe, Jun 15 2008

Status

approved