A binary recurrence sequence \(R_i=R(A,B,R_0,R_1)\) is called balancing sequence if \[ R_1+R_2+\dots+R_{n-1}=R_{n+1}+R_{n+2}+\dots+R_{n+k} \] holds for some \(k\geq 1\) and \(n\geq 2\). The authors prove that there is no balancing sequence of the form \(R_i=R(A,B,0,R_1)\) with \(A^2+4B>0\) except for \((A,B)=(0,1)\). It follows that a Lucas sequence \(R_i=R(A,B,0,1)\) with \(A^2+4B>0\) is not a balancing sequence.