# A song about sequences

Algebra Level pending

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 $$a_{2002} + x$$

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