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What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…?

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What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…?

(a) an = 3an-1−2an+2

(b) an = 3an-1−2an-2

(c) an = 3an-1−2an-1

(d) an = 3an-1−2an-3

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Asked question is from Discrete Probability topic in division Discrete Probability of Discrete Mathematics

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Right answer is (b) an = 3an-1−2an-2

Best explanation: The recurrence relation for the sequence 1, 3, 7, 15, 31, 63,… should be  an = 3an-1−2an-2. The solution for A: A=1/1 − 3x + 2x^2.

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