Let am be the number of strings (of all lengths) with digits in {1, 2, 3} (repeats allowed) such 6. that the sum of the digits in the string is equal to n. (a) Find a recurrence relation satisfied by the an (don't forget the base case(s)). (b) Use your answer to part (a) to prove that an < 2".

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let an be the number of strings (of all lengths) with digits in {1, 2, 3} (repeats allowed) such
that the sum of the digits in the string is equal to n.
(a) Find a recurrence relation satisfied by the an (don't forget the base case(s)).
(b) Use your answer to part (a) to prove that an < 2".
Transcribed Image Text:Let an be the number of strings (of all lengths) with digits in {1, 2, 3} (repeats allowed) such that the sum of the digits in the string is equal to n. (a) Find a recurrence relation satisfied by the an (don't forget the base case(s)). (b) Use your answer to part (a) to prove that an < 2".
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