SE-SKOLORNAS 2003 Problem 6

Consider an infinite square board with an integer written in each square. Assume that for each square the integer in it is equal to the sum of its neighbor to the left and its neighbor above. Assume also that there exists a row $R_0$ in the board such that all numbers in $R_0$ are positive. Denote by $R_1$ the row below $R_0$ , by $R_2$ the row below $R_1$ etc. Show that for each $N \ge 1$ the row $R_N$ cannot contain more than $N$ zeroes.