From The Collaborative International Dictionary of English v.0.48:

Sequence \Se"quence\ (s[=e]"kwens), n. [F. s['e]quence, L.
   sequentia, fr. sequens. See Sequent.]
   1. The state of being sequent; succession; order of
      following; arrangement.
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            How art thou a king
            But by fair sequence and succession?  --Shak.
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            Sequence and series of the seasons of the year.
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   2. That which follows or succeeds as an effect; sequel;
      consequence; result.
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            The inevitable sequences of sin and punishment.
                                                  --Bp. Hall.
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   3. (Philos.) Simple succession, or the coming after in time,
      without asserting or implying causative energy; as, the
      reactions of chemical agents may be conceived as merely
      invariable sequences.
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   4. (Mus.)
      (a) Any succession of chords (or harmonic phrase) rising
          or falling by the regular diatonic degrees in the same
          scale; a succession of similar harmonic steps.
      (b) A melodic phrase or passage successively repeated one
          tone higher; a rosalia.
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   5. (R.C.Ch.) A hymn introduced in the Mass on certain
      festival days, and recited or sung immediately before the
      gospel, and after the gradual or introit, whence the name.
      --Bp. Fitzpatrick.
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            Originally the sequence was called a Prose, because
            its early form was rhythmical prose.  --Shipley.
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   6. (Card Playing)
      (a) (Whist) Three or more cards of the same suit in
          immediately consecutive order of value; as, ace, king,
          and queen; or knave, ten, nine, and eight.
      (b) (Poker) All five cards, of a hand, in consecutive
          order as to value, but not necessarily of the same
          suit; when of one suit, it is called a {sequence
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   7. the specific order of any linear arrangement of items; as,
      the sequence of amino acid residues in a protein; the
      sequence of instructions in a computer program; the
      sequence of acts in a variety show.

From The Collaborative International Dictionary of English v.0.48:

Sequence \Se"quence\, v. t. (Biochem.)
   to determine the sequence of; as, to sequence a protein or a
   DNA fragment.
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