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

Author

T. D. Noe, Jun 15 2008

Keywords

• nonn

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

Programs

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}]