cp's OEIS Frontend

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

%I A217554 #19 Feb 05 2016 20:38:12
%S A217554 3,24,35,48,99,120,168,195,224,288,323,360,440,483,528,675,728,840,
%T A217554 899,1088,1155,1224,1368,1443,1680,1763,1848,2024,2115,2208,2400,2499,
%U A217554 2600,2808,2915,3024,3248,3363,3480,3720,3843,3968,4224,4355,4488,4760,4899
%N A217554 Numbers of the form x^2 - 1 that are the sum of 3 nonzero square numbers.
%C A217554 Solutions of a^2 - b^2 - c^2 - d^2 = 1 with a, b, c, and d positive.
%C A217554 Integer points on the unit sphere in a Minkowski 4-space.
%H A217554 Chai Wah Wu, <a href="/A217554/b217554.txt">Table of n, a(n) for n = 1..10000</a>
%e A217554 3 = 1 + 1 + 1
%e A217554 24 = 16 + 4 + 4
%e A217554 35 = 25 + 9 + 1
%e A217554 48 = 16 + 16 + 16
%e A217554 99 = 81 + 9 + 9
%e A217554 120 = 100 + 16 + 4
%e A217554 168 = 100 + 64 + 4
%e A217554 195 = 169 + 25 + 1
%e A217554 224 = 144 + 64 + 16
%e A217554 288 = 256 + 16 + 16
%e A217554 323 = 289 + 25 + 9
%e A217554 360 = 196 + 100 + 64
%e A217554 440 = 400 + 36 + 4
%e A217554 8 can only be expressed as the sum of 3 squares iff 0 is allowed.
%t A217554 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 A217554 Cf. A169580.
%K A217554 nonn
%O A217554 1,1
%A A217554 _Jon Perry_, Oct 06 2012
%E A217554 Terms a(14)-a(39) from _John W. Layman_, Oct 09 2012