Question 11
(POL 1) Find the number of partitions of the set $\{1,2,\ldots,n\}$ 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.
(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.