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50722 - Scientist's problem

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Section problems

• 50805 - Sum of the weights in a BST
• 50818 - Depth Limited BST
• 50836 - Censored
• 50816 - Largest Sum Path
• 50772 - The Path of a Node
• 50863 - Total Access Cost of a BST
• 50771 - BST Level Sum
• 50773 - Balanced Sum Tree
• 50722 - Scientist's problem

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Prepared by Ilir Capuni. Difficulty Beta

Scientist's problem

Shqip

Question:
A chemist is looking forward to create all possible chains of length n of atoms of Plutonium (Pu) and Lead (Pb), such that each chain that is formed cannot induce an atomic explosion. An explosion could occur if a chain contains at least two consecutive atoms of Plutonium.

For example, for n=4 some of the atomic chains that the scientist can create are:

Pb-Pb-Pu-Pb
Pb-Pb-Pb-Pb
Pu-Pb-Pb-Pu

But the following chain:

Pb-Pu-Pu-Pb

will lead to an explosion, because there are two consecutive Pu atoms.
How many "safe" chains of length n are there?

Input specification
You will be one positive integer n where 1 ≤ n ≤ 35.

Output specification
Show just one integer number: the number of safe chains.

Sample Input I   
  10
Sample Input II   
  16
Sample Output I   
  144
Sample Output II   
  2584


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