Extended Langford Sequences with Small Defects

Ak-extended Langford sequence of defectdand lengthmis a sequences1, s2, …, s2m+1in whichsk=ε, whereεis the null symbol, and each other member of the sequence comes from the set {d, d+1, …, d+m−1}. Eachj∈{d, d+1, …, d+m−1} occurs exactly twice in the sequence, and the two occurrences are separated by exactlyj−1 symbols. In this paper we prove that whend=2, 3, the necessary conditions for the existence of such a sequence are sufficient.