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Search: id:A085690
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| A085690 |
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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. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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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(n-1) (points on surface of cube with square grid on its faces).
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LINKS
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Hugo Pfoertner, FORTRAN program to count intersections.
Dave Seaman, Clive Tooth, Sphere/Cube Intersections. Discussion in Newsgroup sci.math.
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EXAMPLE
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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.
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PROGRAM
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FORTRAN and C# programs are given at the links.
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CROSSREFS
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Cf. A005897, A008574.
Sequence in context: A126176 A074238 A126264 this_sequence A005897 A111694 A129111
Adjacent sequences: A085687 A085688 A085689 this_sequence A085691 A085692 A085693
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 17 2003
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