We introduce a novel fourth order linear recurrence sequence $\{S_n\}$ using the two periodic binary recurrence. We call it ``pellans sequence'' and then we solve the system $$ ab+1=S_x, \quad ac+1=S_y \quad bc+1=S_z $$ where $a<b<c$ are positive integers. Therefore, we extend the order of recurrence sequence for this variant diophantine equations by means of pellans sequence.