The weird one, not directly coded in the genetic code.
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A proteinogenic amino acid is incorporated into proteins during translation. The conventional twenty include glycine, alanine, methionine and proline; they are a subset of amino acids, not a definition of the whole family. [ref]
Nomenclature and Symbolism for Amino Acids and Peptides (Recommendations 1983) by IUPAC-IUB Joint Commission on Biochemical Nomenclature. 3AA-1, Table 1: alpha-amino acids incorporated into protein under mRNA direction