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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb. Автор: Михаил Копачев, РГАТА.
Phalanx-2
There are n castles upon the checkered nxn-sized board, every vertical
line having one castle. Let a horizontal line having at least one castle
be called a bat. The position on the board will be called a phalanx if:
• the castle standing at the leftmost vertical line,
stands also in the lowest horizontal line (and beats it);
• there is no gap between any two castles that separates the
castle from the next or previous
• selecting first left k castles we shall get a regular phalanx of the
width k.
The drawings below show four positions, two of which - those on the left
are phalanxes, and those on the right are not.
Position (c) is not a regular phalanx as the second (unbeaten) horizontal
line separates the second and the third castles from the lower horizontal
line (condition 2 of the above list is not satisfied).
Position (d) is not a regular phalanx: if we take two left castles, they
will not form a regular phalanx (condition 3 of the above list is not satisfied).
Your task is to make a program that will use the specified number n to define
the quantity of different arrangements for castles m, that will be phalanxes.
For example, when n=3, it is possible to have only m=5 phalanxes
(e1)-(e5)
Input
The input contains the only number n.
Output
Output must contain the only number - the answer.
Limitations
0 < n ≤ 18
Input 1
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Output 1
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3
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5
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Input 2
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Output 2
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5
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35
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Для отправки решений необходимо выполнить вход.
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