Let f(n) denote the number of different ways in which the positive integer 'n' can be expressed as sum of 1s and 2s.
for example f(d) = 5 {2 + 2, 2 + 1 + 1, 1 + 2 + 1, 1 + 1 + 2, 1 + 1 + 1 + 1}. Now that order of 1s and 2s is important. Then determine f(f(6))
Text Solution
Verified by Experts377
(377)
Sol. 6 = 3(b) = 6(a) = 1(b) + 4(a) = 2(b) + 2(a)
Number of permutation
1 + 
+ 
+ 
= 13
Now vc f(6) = 13
f(f(6)) = f(13)
13 = 13(a) + 0(b) = 11(a) + 1 = 9(a) + 2(b)
= 7(a) + 3(b) = 5(a) + 4(b) = 3(a) + 5(b) = 1(a) + 6(b)
Total number of ways
1 + 
+ 
+ 
+ 
+ 
+ 
Total = 377
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