Squares that are the sum of 4 unequal squares of Lucas numbers.
25, 49, 100, 169, 900, 2500, 5929, 30276
1
That is, s^2 = l1^2 + l2^2 + l3^2 + l4^2, where the li are Lucas numbers not all equal. This is a finite sequence.
T. D. Noe, Plot of 8 terms
Eric W. Weisstein, MathWorld: Lucas Number
(Mma) nn = 51; PerfectSquareQ[n_] := JacobiSymbol[n, 13] =!= -1 && JacobiSymbol[n, 19] =!= -1 && JacobiSymbol[n, 17] =!= -1 && JacobiSymbol[n, 23] =!= -1 && IntegerQ[Sqrt[n]]; l2 = Table[LucasL[n]^2, {n, 0, nn}]; t = {}; Do[If[a >= b >= c >= d && (a != b || a != c || a != d || b != c || b != d || c != d), n = a + b + c + d; If[PerfectSquareQ[n], AppendTo[t, n]]], {a, l2}, {b, l2}, {c, l2}, {d, l2}]; t
nonn,fini,full
T. D. Noe, Feb 24 2015