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A217554 Numbers of the form x^2 - 1 that are the sum of 3 nonzero square numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A293594 A160665

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

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Last modified January 25 01:44 EST 2020. Contains 331229 sequences. (Running on oeis4.)