[離散] HW7

[roger00 (Stage Column(?))]

有錯請指正，謝謝！

p.455

#2 Find the unique solution for each of the following recurrence relations.

   c) 3*a[n+1] - 4*a[n] = 0  , n ≧ 0 , a[1] = 5

   d) 2*a[n] - 3*a[n-1] = 0  , n ≧ 1 , a[4] = 81

註：　a[n] 中 n 為 a 之下標

p.468

#1 Solve the following recurrence relations. (No final answer should

   involve complex numbers.)

   a) a[n] = 5*a[n-1] + 6*a[n-2]  , n ≧ 2, a[0] = 1, a[1] = 3

   c) a[n+2] + a[n] = 0  , n ≧ 0 , a[0] = 0 , a[1] = 3

   d) a[n] - 6*a[n-1] + 9*a[n-2] = 0  , n ≧ 2 , a[0] = 5 , a[1] = 12

   e) a[n] + 2*a[n-1] + 2*a[n-2] = 0  , n ≧ 2 , a[0] = 1 , a[1] = 3

HW7 第三題 Solve the following recurrence relations.

   a) a[n] + 5*a[n-1] + 8*a[n-2] + 4*a[n-3] = 0  ,

       n ≧ 4 , a[1] = 0 , a[2] = 1 , a[3] = 3

   b) a[n] - 5*a[n-1] + 7*a[n-2] - 3*a[n-3] = 0

       n ≧ 3 , a[0] = -1 , a[1] = 1 , a[2] = 3

p.469

#9 For n ≧ 0, let a[n] count the number of ways a sequence of 1's and 2's

   will sum to n. For example, a[3] = 3 because (1) 1,1,1 ; (2)1,2 ;and (3) 2,1

   sum to 3. Find and solve a recurrence relation for a[n].

#12 Suppose that poker chips come in four colors -- red, white, green, and blue.

    Find and solve a recurrence relation for the number of ways to stack

    n of these poker chips so that there are no consecutive blue chips.


p.470

#24  For n ≧ 1, let a[n] count the number of ways to tile a 2Χn chessboard

     using horizontal (1Χ2) dominoes [which can also be used as vertical

     (2Χ1) dominoes] and square (2Χ2) tiles. Find and solve a recurrence

     relation for a[n].

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