cp's OEIS Frontend

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.

%I A240501 #11 Apr 24 2014 09:37:34
%S A240501 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,
%T A240501 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,
%U A240501 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
%N 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.
%C A240501 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.
%C A240501 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.
%C A240501 See illustrations in links.
%H A240501 Kival Ngaokrajang, <a href="/A240501/a240501.pdf">Illustration R-circle center is at (0.5,0)</a>
%H A240501 Kival Ngaokrajang, <a href="/A240501/a240501_1.pdf">Illustration R-circle center is at (0,0)</a>
%o A240501 (Small Basic)
%o A240501 For r = 2 To 1000 Step 2
%o A240501 c = 0
%o A240501 imax = math.Floor((r-1)/math.Power(3,0.5))
%o A240501 for i = 0 to imax
%o A240501   If Math.Remainder(i,2) = 1 then
%o A240501     j = Math.Power(((r-1)*(r-1)-3*i*i)/4,0.5)
%o A240501   Else
%o A240501     j = (Math.Power((r-1)*(r-1)-3*i*i,0.5)+1)/2
%o A240501   EndIf
%o A240501   If j-math.Floor(j) = 0 Then
%o A240501     If i = 0 Then
%o A240501       c = c + 2
%o A240501     Else
%o A240501       c = c + 4
%o A240501     EndIf
%o A240501   endif
%o A240501 EndFor
%o A240501 TextWindow.Write(c+", ")
%o A240501 EndFor
%Y A240501 Cf. A053416, A053417, A239074.
%K A240501 nonn
%O A240501 1,1
%A A240501 _Kival Ngaokrajang_, Apr 06 2014