Steps

Consider again the machine of the preceding task. How many different ways there are to produce a number $x$?

For example, $x=17$ can be produced in the following ways:

• $1 \rightarrow 2 \rightarrow 4 \rightarrow 7 \rightarrow 14 \rightarrow 17$
• $1 \rightarrow 2 \rightarrow 4 \rightarrow 8 \rightarrow 11 \rightarrow 14 \rightarrow 17$
• $1 \rightarrow 2 \rightarrow 5 \rightarrow 8 \rightarrow 11 \rightarrow 14 \rightarrow 17$
• $1 \rightarrow 4 \rightarrow 7 \rightarrow 14 \rightarrow 17$
• $1 \rightarrow 4 \rightarrow 8 \rightarrow 11 \rightarrow 14 \rightarrow 17$

In this case, the answer is $5$.

In a file allsteps.py, implement the function count_steps that returns the number of ways to produce the number $x$.

The function should be efficient when $x$ is in the range $1 \dots 1000$.

def count_steps(x):
    # TODO

if __name__ == "__main__":
    print(count_steps(1)) # 1
    print(count_steps(2)) # 1
    print(count_steps(3)) # 0
    print(count_steps(4)) # 2
    print(count_steps(5)) # 1
    print(count_steps(17)) # 5
    print(count_steps(42)) # 0
    print(count_steps(100)) # 242
    print(count_steps(1000)) # 2948311