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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. 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 (list; graph; refs; listen; history; text; internal format)
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[{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}];

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 (2-dimensional 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 b-file by Andrew Howroyd, Feb 27 2018

STATUS

approved

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Last modified July 5 07:46 EDT 2020. Contains 335462 sequences. (Running on oeis4.)