

A237707


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


4



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

1,2


LINKS

Rajan Murthy, Table of n, a(n) for n = 1..200
Rajan Murthy, Table of n, a(n), and squared radius for n = 1..200
Rajan Murthy, scilab program for this sequence
Charles R Greathouse IV, Illustration of this sequence


FORMULA

a(n) ~ (Pi*sqrt(30)/25)*n^(3/2).  Charles R Greathouse IV, Mar 14 2014


EXAMPLE

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.


MATHEMATICA

(* Illustrates the sequence *)
Cube[x_, y_, z_]:=Cuboid[{x1, y1, z1}, {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}];
Draw/@Sqrt/@{3, 6, 9, 11, 12, 14} (* Charles R Greathouse IV, Mar 12 2014 *)


PROG

(scilab) See Murthy link.


CROSSREFS

The radii corresponding to the terms are given by the square roots of A000408 starting with squared radius 3.
Cf. A232499 (2dimensional analog).
Sequence in context: A115566 A190507 A087298 * A211642 A127958 A000414
Adjacent sequences: A237704 A237705 A237706 * A237708 A237709 A237710


KEYWORD

nonn


AUTHOR

Rajan Murthy, Feb 11 2014


EXTENSIONS

Duplicate terms deleted by Rajan Murthy, Mar 06 2014
Terms a(36) and beyond added from bfile by Andrew Howroyd, Feb 27 2018


STATUS

approved



