A Langford sequence of order m and defect d can be identified with a labeling of the
vertices of a path of order 2m in which each labeled from d up to d + m - 1 appears twice and in which the vertices that have been label with k are at distance k. In this paper, we introduce two generalizations of this labeling that are related to distances.
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López, S.C., Muntaner-Batle, F.A. Distance labelings: a generalization of Langford sequences. "ARS Mathematica Contemporanea", 5 Gener 2016, vol. 12, núm. 2, p. 235-245.