A016727 Number of inequivalent solutions to x^2+y^2+z^2 = n^2.

1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 3, 2, 5, 1, 4, 4, 4, 2, 7, 3, 4, 2, 5, 3, 9, 2, 5, 5, 5, 1, 11, 4, 7, 4, 6, 4, 10, 2, 7, 7, 7, 3, 13, 4, 7, 2, 9, 5, 14, 3, 8, 9, 10, 2, 16, 5, 9, 5, 9, 5, 21, 1, 11, 11, 10, 4, 17, 7, 10, 4, 11, 6, 18, 4, 16, 10, 11, 2, 23, 7, 12, 7, 14, 7, 20, 3

Offset: 0

Author

csvcjld(AT)nomvst.lsumc.edu

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Michael Gilleland, Some Self-Similar Integer Sequences
• C. D. Olds, On the representations N_3(n^2), Bull. Am. Math. Soc. 47 (6) (1941) 499-503

Crossrefs

Cf. A065458.

Column k=3 of A255212.

Programs

Mathematica

Table[Length[PowersRepresentations[n^2, 3, 2]], {n, 0, 100}]

Formula

a(n) = A000164(n^2). - R. J. Mathar, Feb 12 2017