  We introduce a new four-parameters sequence that simultaneously generalizes
some well-known integer sequences, including Fibonacci, Padovan, Jacobsthatl,
Pell, and Lucas numbers. Combinatorial interpretations are discussed and many
identities for this general sequence are derived. As a consequence, a number of
identities for Fibonacci, Lucas, Pell, Jacobsthal, Padovan, and Narayana
numbers as well as some of their generalizations are obtained. We also present
the Cassini formula for the new sequence.
