A141228 Number of points having maximal visibility in a cubic n x n x n lattice.

1, 8, 1, 8, 20, 64, 20, 32, 64, 216, 13, 432, 64, 64, 20, 32, 8, 32, 32, 216, 64, 64, 27, 8, 64, 216, 7, 32, 64, 352, 32, 216, 8, 8, 125, 64, 8, 24, 1, 8, 64, 8, 32, 24, 8, 8, 27, 8, 8, 8

Offset

1,2

Comments

Sequence A141227 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. Apparently the numbers n in A141226 produce both the n x n and n x n x n lattices having central points with maximum visibility.

Links

Table of n, a(n) for n=1..50.

Mathematica

Table[mx=0; pts=0; Do[cnt=0; Do[If[GCD[d-a, e-b, f-c]<2, cnt++ ], {a, n}, {b, n}, {c, n}]; If[cnt>mx, mx=cnt; pts=1, If[cnt==mx, pts++ ]], {d, n}, {e, n}, {f, n}]; pts, {n, 10}]

Crossrefs

Cf. A141225.

Sequence in context: A081777 A198988 A098367 * A133820 A258718 A019864

Adjacent sequences: A141225 A141226 A141227 * A141229 A141230 A141231

Keyword

nonn

Author

T. D. Noe, Jun 15 2008

Status

approved