A244209 The total number of unit circles (centered at sites of a square lattice with constant 2) intersecting a circle of radius n centered at (0,0).

0, 8, 4, 12, 12, 16, 16, 32, 20, 28, 28, 40, 32, 40, 44, 48, 52, 68, 52, 56, 56, 72, 60, 68, 76, 88, 80, 88, 84, 84, 84, 112, 92, 112, 104, 112, 116, 116, 116, 112, 112, 144, 140, 140, 132, 144, 136, 144, 148, 168, 148, 164, 164, 160, 160, 184, 164, 172, 180, 200, 176, 192, 204

Offset

1,2

Comments

The intersecting and enclosing case found so far only at n = 2. For the cases of enclosing with and without intersecting the sequence would be A168397(n+1) and A168397(n+2) respectively. The first difference seems to be randomly distributed.

Links

Table of n, a(n) for n=1..63.

Kival Ngaokrajang, Illustration of initial terms

Eric Weisstein's World of Mathematics, Circle-Circle Intersection

Prog

(Small Basic)
For n=1 to 200
  count=0
  row=math.Ceiling((n+1)/2)-1
  for i=0 To row
    for j=0 To row
      x=math.power(4*i*i+4*j*j, 1/2)
      c1=-x+1-n
      c2=-x-1+n
      c3=-x+1+n
      c4=x+1+n
      If x>0 and c1*c2*c3*c4>0 then
        c=(1/x)*math.Power(c1*c2*c3*c4, 1/2)
      Else
        c=0
      EndIf
      If c>0 Then
        count=count+1
      EndIf
    EndFor
  EndFor
  If Math.Remainder(n, 2)=0 Then
    circle=4*(count-2)+4
  Else
    circle=4*count
  EndIf
  TextWindow.Writeline(circle)
EndFor

Crossrefs

Cf. A168397.

Sequence in context: A194217 A239971 A082073 * A156279 A203072 A131873

Adjacent sequences: A244206 A244207 A244208 * A244210 A244211 A244212

Keyword

nonn

Author

Kival Ngaokrajang, Jun 22 2014

Extensions

Name specified. - Wolfdieter Lang, Jul 07 2014

Status

approved