cp's OEIS Frontend

A237707 Number of unit cubes, aligned with a three-dimensional Cartesian mesh, completely within the first octant of a sphere centered at the origin, ordered by increasing radius.

%I A237707 #50 Jun 25 2024 02:21:52
%S A237707 1,4,7,10,11,17,20,23,26,32,35,38,44,48,54,60,66,69,75,78,87,96,102,
%T A237707 105,108,114,120,121,127,133,139,145,157,163,169,178,184,196,202,214,
%U A237707 217,220,232,238,241,244,256,263,266,278,284,296,299,308,314,329,332
%N A237707 Number of unit cubes, aligned with a three-dimensional Cartesian mesh, completely within the first octant of a sphere centered at the origin, ordered by increasing radius.
%H A237707 Rajan Murthy, <a href="/A237707/b237707.txt">Table of n, a(n) for n = 1..200</a>
%H A237707 Rajan Murthy, <a href="/A237707/a237707_1.txt">Table of n, a(n), and squared radius for n = 1..200</a>
%H A237707 Rajan Murthy, <a href="/A237707/a237707_2.txt">Scilab program for this sequence</a>
%H A237707 Charles R Greathouse IV, <a href="/A237707/a237707.png">Illustration of this sequence</a>
%F A237707 a(n) ~ (Pi*sqrt(30)/25)*n^(3/2). - _Charles R Greathouse IV_, Mar 14 2014
%e A237707 When the radius of the sphere reaches 3^(1/2), one cube is completely within the sphere. When the radius reaches 6^(1/2), four cubes are completely within the sphere.
%t A237707 (* Illustrates the sequence *)
%t A237707 Cube[x_,y_,z_]:=Cuboid[{x-1,y-1,z-1},{x,y,z}]
%t A237707 Cubes[r_]:=Cube@@#&/@Select[Flatten[Table[{x,y,z},{x,1,r},{y,1,r},{z,1,r}],2],Norm[#]<=r&]
%t A237707 Draw[r_]:=Graphics3D[Union[Cubes[r],{{Green, Opacity[0.3], Sphere[{0,0,0},r]}}],PlotRange->{{0,r},{0,r},{0,r}},ViewPoint->{r,3r/4,3r/5}];
%t A237707 Draw/@Sqrt/@{3,6,9,11,12,14} (* _Charles R Greathouse IV_, Mar 12 2014 *)
%o A237707 (Scilab) // See Murthy link.
%Y A237707 The radii corresponding to the terms are given by the square roots of A000408 starting with squared radius 3.
%Y A237707 Cf. A232499 (2-dimensional analog).
%Y A237707 Partial sums of A014465 and A063691 (but then with repeated terms omitted).
%K A237707 nonn
%O A237707 1,2
%A A237707 _Rajan Murthy_, Feb 11 2014
%E A237707 Duplicate terms deleted by _Rajan Murthy_, Mar 06 2014
%E A237707 Terms a(36) and beyond added from b-file by _Andrew Howroyd_, Feb 27 2018