Let 𝑇(𝑛) be the recurrence relation defined as follows: 𝑇(0) = 1, 𝑇(1) =…

GATE Β· 2024 Β· CS Β· Set 2 Β· Computer Science & IT

Let 𝑇(𝑛) be the recurrence relation defined as follows:

        𝑇(0) = 1,

        𝑇(1) = 2, and

        𝑇(𝑛) = 5𝑇(𝑛 βˆ’ 1) βˆ’ 6𝑇(𝑛 βˆ’ 2) for 𝑛 β‰₯ 2

Which one of the following statements is TRUE?

  1. A.

    𝑇(𝑛) = Θ(2𝑛 )

  2. B.

    𝑇(𝑛) = Θ(𝑛2𝑛 )

  3. C.

    𝑇(𝑛) = Θ(3𝑛)

  4. D.

    𝑇(𝑛) = Θ(𝑛3𝑛)

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