- #1

johnsmiths

- 4

- 0

## Homework Statement

Suppose that a mathematical expression can only be formed by the following symbols: 0, 1,

2, …, 9, ×, +, /. Some examples are “0 + 9”; “2 + 2 × 8”; “1 / 5 + 6”. Let a

_{n}be the the number of such mathematical expression of length n (e.g. “0 + 9” is considered of length 3). Find a recurrence relation for a

_{n}and compute the closed form for a

_{n}.

[Some clarification: We define a number as follows

- 0, 1, 2, …, 9 is a number

- If x is a number, then x0, x1, …, x9 is a number

We define a valid expression as follows

- E is a valid expression if E is a number

- If E, F are valid expressions, then E + F, E × F, E / F are also valid expressions.

For example: 1+50/4 is an expression of length 6, and 09×00/5 is an expression of length 7.]

## The Attempt at a Solution

No idea.