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l < m but a_l > a_m or a_l - l is an odd number

Source: Indian Postal Coaching 2008 set 1 p4

May 25, 2020
combinatoricsoddinequalities

Problem Statement

Let n∈Nn \in N and kk be such that 1≤k≤n1 \le k \le n. Find the number of ordered kk-tuples (a1,a2,...,ak)(a_1, a_2,...,a_k) of integers such the 1≤aj≤n1 \le a_j \le n, for 1≤j≤k1 \le j \le k and either there exist l,m∈{1,2,...,k}l,m \in \{1, 2,..., k\} such that l<ml < m but al>ama_l > a_m or there exists l∈{1,2,...,k}l \in \{1, 2,..., k\} such that al−la_l - l is an odd number.
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