Final answer:
The sequence ℓ is defined recursively, and its values can be found by using its definition. ℓ₁ is 0, ℓ₃ is calculated as 3, and ℓ₄ is computed as 6 using previous terms in the sequence.
Step-by-step explanation:
The sequence defined by c₁ = 0, and cn = c⌊n/2⌋ + n, for all n > 1, can be computed as follows:
c₁ = 0, is provided as the initial condition.
For c₃, we find the floor of 3/2, which is 1, and compute c₃ = c₁ + 3. Since we have that c₁ = 0, it follows that c₃ = 0 + 3 = 3.
In the case of c₄, the floor of 4/2 is 2. We need to compute c₂ to determine c₄. For c₂, the floor of 2/2 is 1, so c₂ = c₁ + 2 = 0 + 2 = 2. Now we can compute c₄ = c₂ + 4 = 2 + 4 = 6.
By following the given formula, each term can be found using the value of its preceding term(s) and the recursive definition provided.