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

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Formula

a(n) = number of b(i) <= n^2, b() = A000378.

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} ]

Crossrefs

Cf. A047808, A000378.

Sequence in context: A011904 A308265 A218914 * A014126 A019450 A098169

Adjacent sequences: A047806 A047807 A047808 * A047810 A047811 A047812

Keyword

nonn,easy,nice

Author

Wouter Meeussen,David W. Wilson

Status

approved