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In this work, we consider the sequence whose  n th  term is the number of h -vectors of length n . The set of integer vectors E ( n )  is introduced. For, n  >= 2, the cardinality of  E ( n ) is the n th  Lucas number L n  is showed. The relation between the set of h -vectors  L ( n ) and the set of integer vectors  E ( n ) is given.

A Sequence Bounded Above by the Lucas Numbers