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

1,1

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

Table of n, a(n) for n=1..144.

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

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

Prog

(Small Basic)
For r = 2 To 1000 Step 2
c = 0
imax = math.Floor((r-1)/math.Power(3, 0.5))
for i = 0 to imax
  If Math.Remainder(i, 2) = 1 then
    j = Math.Power(((r-1)*(r-1)-3*i*i)/4, 0.5)
  Else
    j = (Math.Power((r-1)*(r-1)-3*i*i, 0.5)+1)/2
  EndIf
  If j-math.Floor(j) = 0 Then
    If i = 0 Then
      c = c + 2
    Else
      c = c + 4
    EndIf
  endif
EndFor
TextWindow.Write(c+", ")
EndFor

Crossrefs

Cf. A053416, A053417, A239074.

Sequence in context: A241460 A167568 A361301 * A278251 A286847 A291439

Adjacent sequences: A240498 A240499 A240500 * A240502 A240503 A240504

Keyword

nonn

Author

Kival Ngaokrajang, Apr 06 2014

Status

approved