A217554 - OEIS

%I #19 Feb 05 2016 20:38:12

%S 3,24,35,48,99,120,168,195,224,288,323,360,440,483,528,675,728,840,

%T 899,1088,1155,1224,1368,1443,1680,1763,1848,2024,2115,2208,2400,2499,

%U 2600,2808,2915,3024,3248,3363,3480,3720,3843,3968,4224,4355,4488,4760,4899

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

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

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

%H Chai Wah Wu, <a href="/A217554/b217554.txt">Table of n, a(n) for n = 1..10000</a>

%e 3 = 1 + 1 + 1

%e 24 = 16 + 4 + 4

%e 35 = 25 + 9 + 1

%e 48 = 16 + 16 + 16

%e 99 = 81 + 9 + 9

%e 120 = 100 + 16 + 4

%e 168 = 100 + 64 + 4

%e 195 = 169 + 25 + 1

%e 224 = 144 + 64 + 16

%e 288 = 256 + 16 + 16

%e 323 = 289 + 25 + 9

%e 360 = 196 + 100 + 64

%e 440 = 400 + 36 + 4

%e 8 can only be expressed as the sum of 3 squares iff 0 is allowed.

%t 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 *)

%Y Cf. A169580.

%K nonn

%O 1,1

%A _Jon Perry_, Oct 06 2012

%E Terms a(14)-a(39) from _John W. Layman_, Oct 09 2012