Let (G_m)_m≥0 be an integer linear recurrence sequence (satisfying some weak technical conditions) and let x ≥ 1 be an integer. In this paper, among other things, we are interested in non-consecutive combinations xG_n+a + G_n that belong to the sequence (G_m)_m≥0 for infinitely many positive integers n. In this case, we make explicit an upper bound for x that depends only on a and the zeros of the characteristic polynomial of this recurrence (this generalizes previous papers of Trojovský). As an application, we study the Fibonacci case.