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A n-substring of a number is a substring of its digits that sum to n. For example, the 8-substrings of the number 352114 are:

A number is called 8-substring-friendly if every one of its digits belongs to a 8-substring. For example, 352114 is 8-substring-friendly, but 26(5)44 is not. For a given n, find T(n) the number of ...