Palindromic Numbers

A palindromic number is the same when it is written backwards.
Examples are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 441, 55, 66,77, 88, 99, 101, 111, 121, 131, ...
Any single digit number can appear in a palindromic number.
A palindromic number can have any number of digits. If there is an odd number of digits the middle digit must appear an odd number of times, and if there are an even number of digits, then each single digit number must appear an even number of times.
However many digits there are the number must be symmetric about the middle, in the sense that the first and last numbers must be the same, the second and second from last are the same and so on.