+1 vote
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Given a integer N greater than zero.

How many sequences of 1's and 2's are there such that sum of the numbers in the sequence = N ?

(not necessary that every sequence must contain both 1 and 2 )

example :

for N = 2 ; 11,2 => ans = 2 sequences of 1's and 2's

for N = 3 ; 11,12,21 => ans = 3 sequences of 1's and 2's
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It is (N+1)th fibonacci number.

Observe the pattern: http://ideone.com/QLb1CZ

selected
thanks this can be solved by dynamic as well as generating function or matrix exponentiation. similar to domino tiling
Yes, the recurrence relation is $F(0) = 1$, $F(1) = 1$ and $F(n) = F(n-1) + F(n-2)$, $\forall$ $n$ $\geq$ $2$.
@Air1. Hats off bro for you thought about the recurrance :)
The chapter on generating function from concrete mathematics, well described for this kind of problem.