Count sorted vowel strings: math approach

[vbrazo]

Given an integer n, return the number of strings of length n that consist only of vowels (a, e, i, o, u) and are lexicographically sorted.

A string s is lexicographically sorted if for all valid i, s[i] is the same as or comes before s[i + 1] in the alphabet.

# Example 1:
#
# Input: n = 1
# Output: 5
# Explanation: The 5 sorted strings that consist of vowels only are ["a","e","i","o","u"].
#
# Example 2:
#
# Input: n = 2
# Output: 15
# Explanation: The 15 sorted strings that consist of vowels only are
# ["aa","ae","ai","ao","au","ee","ei","eo","eu","ii","io","iu","oo","ou","uu"].
# Note that "ea" is not a valid string since 'e' comes after 'a' in the alphabet.
#
# Example 3:
#
# Input: n = 33
# Output: 66045