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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 25 12:36 EDT 2019. Contains 322456 sequences. (Running on oeis4.)