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A065089 Volume (multiplied by 3) of polyhedron formed by points (i,j,k) in Z^3 with i^2+j^2+k^2 = n^2. 1
0, 4, 32, 272, 256, 1156, 2176, 3692, 2048, 8496, 9248, 15196, 17408, 22324, 29536, 39820, 16384, 56144, 67968, 79252, 73984, 111956, 121568, 143176, 139264, 184852, 178592, 238884, 236288, 285940, 318560, 358004, 131072, 435396, 449152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n=2^k, a(n)=4 n^3 because A016727(2^k) = SumOfSquaresRepresentations[3,(2^k)^2] contains only {0,0,2^k}.

This is why a(16) and a(32) are visibly so much smaller than their neighbors when you look at the graph. [Jonathan Vos Post, Apr 22 2011]

LINKS

Table of n, a(n) for n=0..34.

EXAMPLE

a(2) = 32 because the volume of the polyhedron formed by all integer points at distance 2 from the origin, {{-2, 0, 0}, {0, -2, 0}, {0, 0, -2}, {0, 0, 2}, {0, 2, 0}, {2, 0, 0}}, is 32/3.

MATHEMATICA

forms[ z:{_Integer, _, _} ] := Union[ Flatten[ Permutations/@(Times[ z, # ]&/@Flatten[ Outer[ List, {1, -1}, {1, -1}, {1, -1} ], 2 ]), 1 ] ]; polyhedra=Flatten[ forms/@SumOfSquaresRepresentations[ 3, # ], 1 ]&/@(Range[ 1, 36 ]^2); HullVolume[ #, ConvexHull3D[ # ] ]&/@polyhedra;

CROSSREFS

Cf. A016727.

Sequence in context: A013731 A009509 A036725 * A113329 A246818 A145710

Adjacent sequences: A065086 A065087 A065088 * A065090 A065091 A065092

KEYWORD

nonn

AUTHOR

Wouter Meeussen, Nov 10 2001

STATUS

approved

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Last modified December 2 19:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)