有错请指正，谢谢！ 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 注：　a[n] 中 n 为 a 之下标 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 第三题 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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