Given an integer array nums
, return the number of all the arithmetic subsequences of nums
.
A sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.
- For example,
[1, 3, 5, 7, 9]
,[7, 7, 7, 7]
, and[3, -1, -5, -9]
are arithmetic sequences. - For example,
[1, 1, 2, 5, 7]
is not an arithmetic sequence.
A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.
- For example,
[2,5,10]
is a subsequence of[1,2,1,**2**,4,1,**5**,**10**]
.
The answer is guaranteed to fit in 32-bit integer.
Example 1:
Input: nums = [2,4,6,8,10]
Output: 7
Explanation: All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]
Example 2:
Input: nums = [7,7,7,7,7]
Output: 16
Explanation: Any subsequence of this array is arithmetic.
Constraints:
1 <= nums.length <= 1000
- -231 <= nums[i] <= 231 - 1