|
Search: id:A065089
|
|
|
| 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. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
For n=2^k, a(n)=4 n^3 because A016727(2^k)=SumOfSquaresRepresentations[3,(2^k)^2] contains only {0,0,2^k};
|
|
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: A092811 A009509 A036725 this_sequence A113329 A145710 A110901
Adjacent sequences: A065086 A065087 A065088 this_sequence A065090 A065091 A065092
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 10 2001
|
|
|
Search completed in 0.002 seconds
|
