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 A303743 a(n) is a number of lattice points in 3D Cartesian grid between cube with edge length 2*n centered in origin and its inscribed sphere. Three pairs of the cube's faces are parallel to the planes XOY, XOZ, YOZ respectively. 0
 0, 0, 8, 92, 220, 412, 784, 1272, 1848, 2696, 3692, 5020, 6460, 8176, 10248, 12720, 15464, 18476, 21988, 25924, 30016, 35040, 40248, 46052, 52388, 59132, 66364, 74416, 83256, 92304, 102500, 112988, 124076, 136252, 148936, 162648, 176928, 192332, 208100, 225284, 243088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If two parallel faces of the inscribed cube are parallel XOY-plane and other two pairs are parallel planes x=y and x=-y respectively we'll have another sequence. LINKS FORMULA a(n) = A016755(n-1) - A000605(n) - 6. EXAMPLE For n=3 we have 8 points between the defined cube and its inscribed sphere:   (-2,-2,-2)   (-2,-2, 2)   (-2, 2,-2)   (-2, 2, 2)   ( 2,-2,-2)   ( 2,-2, 2)   ( 2, 2,-2)   ( 2, 2, 2) PROG (Python) for n in range (1, 42): .count=0 ..for x in range (-n, n): ...for y in range (-n, n): ....for z in range (-n, n): .....if (x*x+y*y+z*z>n*n and x>-n and x-n and y-n and zn^2))); \\ Michel Marcus, Jun 23 2018 CROSSREFS Cf. A000605, A016755. For the 2D case see A303642. Sequence in context: A298013 A302614 A220573 * A187157 A332597 A331448 Adjacent sequences:  A303740 A303741 A303742 * A303744 A303745 A303746 KEYWORD nonn AUTHOR Kirill Ustyantsev, Apr 29 2018 STATUS approved

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Last modified April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)