A240501 Given circular disks of radius r in a hexagonal lattice covered by a circular disk of radius R = r*2n, if the center of the circle is chosen at the middle between two lattice points, a(n) is the number of points at which an r-circle is tangent to the R-circle.

2, 2, 2, 6, 2, 2, 6, 2, 2, 6, 6, 2, 2, 2, 2, 6, 2, 6, 6, 6, 2, 6, 2, 2, 10, 2, 2, 2, 6, 2, 6, 6, 6, 6, 2, 2, 6, 2, 6, 6, 2, 2, 2, 2, 2, 18, 6, 6, 6, 2, 2, 6, 6, 2, 6, 6, 2, 2, 6, 6, 2, 2, 2, 6, 6, 2, 18, 2, 2, 6, 2, 6, 2, 10, 2, 6, 2, 6, 6, 2, 6, 6, 2, 2, 10, 6, 2, 6, 2, 2, 6, 6, 6, 2, 6, 2, 6, 6, 2, 6, 6, 6, 2, 2, 6, 6, 2, 6, 18, 6, 6, 6, 2, 2, 6, 6, 2, 2, 6, 2, 6, 2, 10, 18, 2, 2, 2, 2, 2, 18, 2, 2, 2, 2, 2, 6, 18, 2, 6, 6, 2, 6, 6, 6

Offset: 1

Author

Kival Ngaokrajang, Apr 06 2014

Keywords

• nonn

Comments

a(n) are even R that give a(n) >= 2, which seems to be nonperiodic, for even R there is no contact point exist. This is the case of A053417.

Sequence A053416 addresses the case in which the center of the R-circle (R = r*n) is chosen at a lattice point instead; in that case, the number of contact points is 0 and 6 for even n > 0 and odd n > 1, respectively.

See illustrations in links.

Links

• Kival Ngaokrajang, Illustration R-circle center is at (0.5,0)
• Kival Ngaokrajang, Illustration R-circle center is at (0,0)

Crossrefs

Cf. A053416, A053417, A239074.