Problem 3. 6 marks] a chord is a string of length either one or two, over the alphabet a, b, c. d, e, f, g. b, }, in which the first character must be a letter, and the second character, if it exists, must be either b or # examples of chords include: a db g b examples of strings that are not chords include: #c fg bb a valid chord sequence is a string of characters containing chords and whitespace, where each pair of chords is separated by a single space, and there is no leading or trailing whitespace. the length of a chord sequence is the number of characters, including spaces, in that sequence. examples of chord sequences (and their corresponding lengths) are 6 c ab f d g (length 11) b (length 1) ed a c (length 7) examples of strings that are not chord sequences are abc cab f d g g let an be the number of chord sequences of length n (a) find a1, a2, a3, and a4. (b) give (with justification) an expression for a in terms of a-2 and a-3, that works for all n 2 4 (c) prove, by induction on n, that an 3.8" for all n2.