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+1 vote
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
asked in Combinatory by Veteran (57.4k points)
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1 Answer

+3 votes
Best answer

It is (N+1)th fibonacci number.

Observe the pattern:

answered by Loyal (3.7k points)
selected by
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.

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