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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).

%I A244209 #16 Feb 16 2025 08:33:22
%S A244209 0,8,4,12,12,16,16,32,20,28,28,40,32,40,44,48,52,68,52,56,56,72,60,68,
%T A244209 76,88,80,88,84,84,84,112,92,112,104,112,116,116,116,112,112,144,140,
%U A244209 140,132,144,136,144,148,168,148,164,164,160,160,184,164,172,180,200,176,192,204
%N 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).
%C A244209 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.
%H A244209 Kival Ngaokrajang, <a href="/A244209/a244209.pdf">Illustration of initial terms</a>
%H A244209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Circle-CircleIntersection.html">Circle-Circle Intersection</a>
%o A244209 (Small Basic)
%o A244209 For n=1 to 200
%o A244209   count=0
%o A244209   row=math.Ceiling((n+1)/2)-1
%o A244209   for i=0 To row
%o A244209     for j=0 To row
%o A244209       x=math.power(4*i*i+4*j*j,1/2)
%o A244209       c1=-x+1-n
%o A244209       c2=-x-1+n
%o A244209       c3=-x+1+n
%o A244209       c4=x+1+n
%o A244209       If x>0 and c1*c2*c3*c4>0 then
%o A244209         c=(1/x)*math.Power(c1*c2*c3*c4,1/2)
%o A244209       Else
%o A244209         c=0
%o A244209       EndIf
%o A244209       If c>0 Then
%o A244209         count=count+1
%o A244209       EndIf
%o A244209     EndFor
%o A244209   EndFor
%o A244209   If Math.Remainder(n,2)=0 Then
%o A244209     circle=4*(count-2)+4
%o A244209   Else
%o A244209     circle=4*count
%o A244209   EndIf
%o A244209   TextWindow.Writeline(circle)
%o A244209 EndFor
%Y A244209 Cf. A168397.
%K A244209 nonn
%O A244209 1,2
%A A244209 _Kival Ngaokrajang_, Jun 22 2014
%E A244209 Name specified. - _Wolfdieter Lang_, Jul 07 2014