

A085690


Number of intersections between a sphere inscribed in a cube and the n X n X n cubes resulting from a cubic lattice subdivision of the enclosing cube.


2



8, 26, 56, 98, 152, 194, 272, 362, 440, 530, 656, 746, 872, 1034, 1160, 1298, 1496, 1658, 1856, 1994, 2240, 2450, 2624, 2906, 3128, 3362, 3656, 3890, 4208, 4442, 4760, 5090, 5360, 5714, 6032, 6362, 6752, 7106, 7496, 7826, 8216, 8618, 9080, 9458, 9896
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OFFSET

2,1


COMMENTS

A concise description of the problem is given by Clive Tooth in the Seaman, Tooth link. Sequence terms up to n=10 were first given by Dave Seaman. Cubes having at least one vertex on the sphere and all other vertices either all inside or all outside the sphere are counted as 1/2. a(n) is asymptotic to (3/2)*pi*n^2. (Clive Tooth) The terms a(2),..,a(6) are identical with A005897(n1) (points on surface of cube with square grid on its faces).


LINKS

Hugo Pfoertner, Table of n, a(n) for n = 2..1000
Hugo Pfoertner, FORTRAN program to count intersections.
Dave Seaman, Clive Tooth, Sphere/Cube Intersections. Discussion in Newsgroup sci.math.


EXAMPLE

a(2)=8 because all 8 cubes resulting from a 2*2*2 subdivision of a cube are intersected by a sphere inscribed in the large cube.
a(4)=56: 8 central cubes of 4*4*4=64 not intersected.


PROG

FORTRAN and C# programs are given at the links.


CROSSREFS

Cf. A005897, A008574.
Sequence in context: A074238 A126264 A225274 * A005897 A215097 A111694
Adjacent sequences: A085687 A085688 A085689 * A085691 A085692 A085693


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jul 17 2003


EXTENSIONS

Corrected overflow in program and bfile by Hugo Pfoertner, Apr 09 2016


STATUS

approved



