Unlucky Numbers

A bus ticket with a $6$-digit number is traditionally considered lucky if the sum of its first three digits equals the sum of its last three digits. Schoolboy Vasya loved getting lucky tickets, but it did not happen often. So, he decided to change the definition for himself: a ticket is considered lucky if the sum of some of its digits equals the sum of the remaining digits. For example, Vasya considers the ticket number $561743$ lucky because 5 + 1 + 4 + 3 = 6 + 7.

As Vasya grew up, he continued to try to find lucky numbers in various document numbers. He extended his definition for $n$-digit numbers composed of digits from $0$ to $k$ (1 \leq k \leq 9). A document number is considered lucky if the sum of some of its digits equals the sum of the remaining digits. All other numbers are considered unlucky. Despite the extended definition, many numbers still remain unlucky.

You are asked to determine the number of unlucky $n$-digit numbers that can be formed using digits from $0$ to $k$. Numbers may have any number of leading zeros.