Squares that are the sum of 4 different squares of Fibonacci numbers, with 1 being the least.
196, 1225, 8100, 54756, 373321, 2553604, 17489124, 119836809, 821280964, 5628900676, 38580423561, 264432492900, 1812442912900, 12422657127241, 85146128781156, 583600170521124, 4000054871604169, 27416783424740164, 187917427776935844
1
That is, the terms are (f(2n-1) + 1)^2 = f(2n-1)^2 + f(n+1)^2 + f(n-2)^2 + f(1)^2. These terms satisfy a 5-order linear recursion: a(n) = 11*a(n-1) - 33*a(n-2) + 33*a(n-3) - 11*a(n-4) + a(n-5).
T. D. Noe, Plot of 200 terms
T. D. Noe, Table of 200 terms
Eric W. Weisstein, MathWorld: Fibonacci Number
Eric W. Weisstein, MathWorld: Linear Recurrence Equation
(Mma) nn = 45; f2 = Table[Fibonacci[n]^2, {n, nn}]; Table[f2[[2*n - 1]] + f2[[n + 1]] + f2[[n - 2]] + f2[[1]], {n, 4, Floor[nn/2]}]
nonn
T. D. Noe, Feb 18 2015