A047809 a(n) counts different values of i^2+j^2+k^2 <= n^2 or number of distances from the origin to all integer points inside a sphere of radius n.
1, 2, 5, 9, 15, 23, 32, 43, 55, 70, 86, 103, 122, 143, 166, 190, 215, 243, 273, 304, 336, 371, 406, 443, 482, 523, 566, 611, 656, 704, 753, 803, 855, 910, 966, 1024, 1083, 1145, 1207, 1270, 1336, 1404, 1474, 1544, 1616, 1690, 1766, 1843, 1922, 2004
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
Table[ Length@Union@Flatten@Table[ i^2+j^2+k^2, {i, 0, n}, {j, 0, Min[ i, Floor[ Sqrt[ n^2-i^2 ] ] ]}, {k, 0, Min[ j, Floor[ Sqrt[ n^2-i^2-j^2 ] ] ]} ], {n, 0, 64} ]
Formula
a(n) = number of b(i) <= n^2, b() = A000378.