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A237707
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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.
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5
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1, 4, 7, 10, 11, 17, 20, 23, 26, 32, 35, 38, 44, 48, 54, 60, 66, 69, 75, 78, 87, 96, 102, 105, 108, 114, 120, 121, 127, 133, 139, 145, 157, 163, 169, 178, 184, 196, 202, 214, 217, 220, 232, 238, 241, 244, 256, 263, 266, 278, 284, 296, 299, 308, 314, 329, 332
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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(* Illustrates the sequence *)
Cube[x_, y_, z_]:=Cuboid[{x-1, y-1, z-1}, {x, y, z}]
Cubes[r_]:=Cube@@#&/@Select[Flatten[Table[{x, y, z}, {x, 1, r}, {y, 1, r}, {z, 1, r}], 2], Norm[#]<=r&]
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}];
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PROG
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(scilab) See Murthy link.
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CROSSREFS
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The radii corresponding to the terms are given by the square roots of A000408 starting with squared radius 3.
Cf. A232499 (2-dimensional analog).
Partial sums of A014465 and A063691 (but then with repeated terms omitted).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Terms a(36) and beyond added from b-file by Andrew Howroyd, Feb 27 2018
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STATUS
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approved
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