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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
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: A363440 A009509 A036725 * A113329 A246818 A145710
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Nov 10 2001
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)