SOLUTION: According to the following sequence for first 997th terms, how many odd number(s) is / are there? 1, 2, 3, 6, 11, 20, 37, 68, …

Question 1146551: According to the following sequence for first 997th terms, how many odd number(s) is / are there?
1, 2, 3, 6, 11, 20, 37, 68, …
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

We are given only the first few terms of the sequence with no other information about what kind of sequence it is. That means the subsequent terms could be anything; it is impossible to know what the sequence is. So it is impossible to know how many odd terms there are.

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Added later, after a response from the reader....

In fact, this is called the Tribonacci sequence -- like the Fibonacci sequence, except each term is the sum of the previous THREE terms.

I don't know much about the Tribonacci sequence -- things like a formula for the n-th term.

But determining the pattern of odd and even terms is easy:

1st term: odd
2nd term: even
3rd term: odd
4th term: odd+even+odd = even
5th term: even+odd+even = odd
6th term: odd+even+odd = even
7th term: even+odd+even = odd
...

It should be clear that the terms alternate between odd and even. So with the first term being odd, the first 997 terms will consist of 499 odd terms and 498 even terms.
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