Further to my reply to sibling-reply finnw, here's the pattern of digits, further showing his 10 * 9, etc., breakdown.

    $ pins |
    > sed -r '
    >     :a; s/^([0-9])(.*)\1/\1\2a/; ta; s/[0-9]/a/
    >     :b; s/a([0-9])(.*)\1/a\1\2b/; tb; s/[0-9]/b/
    >     s/([0-9])\1/cc/; s/[0-9]/c/
    >     s/[0-9]/d/
    > ' |
    > sort | uniq -c | sort -n
         10 aaaa
         90 aaab
         90 aaba
         90 aabb
         90 abaa
         90 abab
         90 abba
         90 abbb
        720 aabc
        720 abac
        720 abbc
        720 abca
        720 abcb
        720 abcc
       5040 abcd
    $