A179334 Squares that are the sum of three positive Fibonacci numbers.
4, 9, 16, 25, 36, 49, 64, 81, 100, 144, 256, 289, 324, 400, 529, 576, 625, 1024, 1089, 1225, 1369, 1600, 2209, 3249, 7396, 12544, 15129, 19321, 46656, 103684, 710649, 1347921, 2178576, 4870849, 14930496, 24990001, 33385284, 228826129, 1568397609, 10749957124
Offset: 1
Keywords
Examples
a(5) = 36 = 1+1+34 = Fib(1)+Fib(2)+Fib(9).
Links
- Robert Israel, Table of n, a(n) for n = 1..100
Programs
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Maple
phi:= 1/2 + sqrt(5)/2: fib:= combinat:-fibonacci: invfib := proc(x::posint) local q, n; q:= evalf((ln(x+1/2) + ln(5)/2)/ln(phi)); n:= floor(q); if fib(n) <= x then while fib(n+1) <= x do n := n+1 end do else while fib(n) > x do n := n-1 end do end if; n end: g:= proc(n) local ct,x,y,R; ct:= 0; x:= n^2; R:=NULL; while x > 0 do y:= invfib(x); ct:= ct+1; if ct = 4 then return [false, max(n+1,isqrt(fib(R[1])+fib(R[2]) + fib(R[3]+1)))] fi; R:= R, y; x:= x - fib(y) od; if ct < 3 then [true,n+1] else [true, max(n+1,isqrt(fib(R[1])+fib(R[2])+fib(R[3]+1)))] fi end proc: R:= NULL: count:= 0: n:= 2: while count < 40 do V:= g(n); if V[1] then R:= R, n^2; count:= count+1; fi; n:= V[2]; od: R; # Robert Israel, Aug 20 2025 -
Mathematica
f=Fibonacci[Range[40]]; Select[Union[Flatten[Outer[Plus, f, f, f]]], #
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