# Any idea about Images of a Function?

Algebra Level 5

Let $$f$$ be a function from the set of all non-negative integers into itself such that:

• $$(f(2n+1))^2 - (f(2n))^2 = 6f(n) + 1$$, and

• $$f(2n) \geq f(n)$$

How many numbers less than $$2015$$ are there in the image of $$f$$?

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