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we are given five different tiles two of size wXI and three of size 2 * 1 TA BC D and LE to tike a horizontal strip ofn boxes . Let a (n ) be the member of different filings of the strip of n boxes for hyo For example. the possible filings when n= 2 are AA JAB BJA B B C D JE Hence a ( 2 ) = 7 a) compute the numbers a(n) for ownzy b) Explain why a (n) = 20 (n -1) + 3 a ( n-2) for n > 2 ( ) Let A( 2 ) = Enzo a (n) z" be the generating function for a(n ) . Prove that A ( 2 ) = 32 427 d ) 1-23- 326 =-1+ 1-28-375 find a closed formula for a (), when my