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1. Counting alternating-parity increasing sequences ●●●○○ 50 ptsA finite strictly increasing sequence of integers is called alternating if its first term is odd, its second term is even, its third term is odd, and so on, alternating in parity. The empty sequence also counts as alternating. Let $A(n)$ be the number of alternating sequences whose terms are all taken from $\{1,2,\ldots,n\}$, so $A(1)=2$ and $A(2)=3$. Find $A(20)$.