A song about sequences

Let $(a_n)_{n \in \mathbb{N}}$ be a monotone increasing sequences of non negative integers. The sequence has the property, that each non-negative integer has a unique representation in the form of $a_i + 2*a_j + 4*a_k$

$a_i , a_j, a_k$ don't have to be distinct.

Let x be the number of sequences that suffice the given property above.

Compute $a_{2002} + x$