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

1,1

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A169580.

Sequence in context: A123598 A106217 A267274 * A278491 A363536 A293594

Adjacent sequences: A217551 A217552 A217553 * A217555 A217556 A217557

Keyword

nonn

Author

Jon Perry, Oct 06 2012

Extensions

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

Status

approved