IMO Shortlist 1987 problem 11

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Dodao/la: arhiva
2. travnja 2012.
Find the number of partitions of the set \{1, 2, \cdots, n\} into three subsets A_1,A_2,A_3, some of which may be empty, such that the following conditions are satisfied:

(i) After the elements of every subset have been put in ascending order, every two consecutive elements of any subset have different parity.

(ii) If A_1,A_2,A_3 are all nonempty, then in exactly one of them the minimal number is even .

Proposed by Poland.
Izvor: Međunarodna matematička olimpijada, shortlist 1987