A217554 Numbers of the form x^2 - 1 that are the sum of 3 nonzero square numbers.

3, 24, 35, 48, 99, 120, 168, 195, 224, 288, 323, 360, 440, 483, 528, 675, 728, 840, 899, 1088, 1155, 1224, 1368, 1443, 1680, 1763, 1848, 2024, 2115, 2208, 2400, 2499, 2600, 2808, 2915, 3024, 3248, 3363, 3480, 3720, 3843, 3968, 4224, 4355, 4488, 4760, 4899

Offset: 1

Author

Jon Perry, Oct 06 2012

Keywords

• nonn

Comments

Solutions of a^2 - b^2 - c^2 - d^2 = 1 with a, b, c, and d positive.

Integer points on the unit sphere in a Minkowski 4-space.

Examples

			3 = 1 + 1 + 1
24 = 16 + 4 + 4
35 = 25 + 9 + 1
48 = 16 + 16 + 16
99 = 81 + 9 + 9
120 = 100 + 16 + 4
168 = 100 + 64 + 4
195 = 169 + 25 + 1
224 = 144 + 64 + 16
288 = 256 + 16 + 16
323 = 289 + 25 + 9
360 = 196 + 100 + 64
440 = 400 + 36 + 4
8 can only be expressed as the sum of 3 squares iff 0 is allowed.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A169580.

Programs

Mathematica

nn = 100; t = {}; Do[n = a^2 + b^2 + c^2; If[n <= nn^2 + 2 && IntegerQ[Sqrt[n + 1]], AppendTo[t, n]], {a, nn}, {b, a}, {c, b}]; t = Union[t] (* T. D. Noe, Oct 10 2012 *)

Extensions

Terms a(14)-a(39) from John W. Layman, Oct 09 2012