- #1
Dragonfall
- 1,030
- 4
Given positive interger N, now many non-decreasing sequences of length N are there whose entries are less than N?
A non-decreasing sequence is a sequence of numbers in which each subsequent number is equal to or greater than the previous number.
Yes, a non-decreasing sequence can contain repeated numbers as long as the sequence remains non-decreasing.
The maximum length of a non-decreasing sequence is equal to the given positive integer N.
The number of non-decreasing sequences that can be created from a given positive integer N is equal to (N+1) choose 2, which can be calculated using the binomial coefficient formula.
Yes, a non-decreasing sequence can start with any number as long as the sequence remains non-decreasing.