Let E be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let P=(x₁/z₁²,y₁/z₁³) be a rational point of infinite order on E, where x₁,y₁,z₁ are coprime integers. We show that the integer sequence (z_n)_n≧1 defined by nP=(x_n/z_n²,y_n/z_n³) for all n≧ 1 does not eventually coincide with (u_n²)_n≧1 for any choice of linear recurrence sequence (u_n)_n≧1 with integer values.