A396333 Number of ordered triples of integers (x,y,z) with 0 <= x <= y <= z and x^2 + y^2 + z^2 < n^2.

0, 1, 4, 8, 15, 25, 40, 56, 79, 106, 141, 179, 224, 278, 341, 408, 488, 572, 672, 779, 899, 1028, 1169, 1324, 1491, 1669, 1869, 2077, 2306, 2539, 2800, 3064, 3363, 3668, 3996, 4341, 4705, 5090, 5489, 5916, 6364, 6825, 7323, 7834, 8377, 8937, 9524, 10127, 10764

Offset

0,3

Links

David A. Corneth, Table of n, a(n) for n = 0..4999

Formula

The sequence a(n)/n^3 converges to Pi/36 as n->oo.

Example

The integer triples (x,y,z) with 0 <= x <= y <= z and x^2 + y^2 + z^2 < 2^2 are exactly [0, 0, 0], [0, 0, 1], [0, 1, 1] and [1, 1, 1], so a(2) = 4.

Prog

(PARI) a(n) = sum(z=0, n, sum(y=0, z, sum(x=0, y, x^2+y^2+z^2 < n^2)))

Crossrefs

Cf. A000605, A078183, A117609, A255212, A394684.

Sequence in context: A333266 A024624 A350162 * A098196 A027961 A348897

Adjacent sequences: A396330 A396331 A396332 * A396334 A396335 A396336

Keyword

nonn

Author

Jean-Marc Rebert, May 22 2026

Status

approved