Irmak, NurettinAlp, Murat2019-08-012019-08-0120160350-1302https://dx.doi.org/10.2298/PIM1614259Ihttps://hdl.handle.net/11480/3725We 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, ac + 1 = S-y 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.eninfo:eu-repo/semantics/closedAccessDiophantine triplespell numbersbalancing numberspellans sequenceArticle10011425926910.2298/PIM1614259I2-s2.0-85002755206Q4WOS:000398279100018N/A