SOLUTION: Can you please help me solve this question? Many of the terms have a # or a letter with a # or letter written just below it. I will use "sub" showing what is written that is lowe

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Question 891573: Can you please help me solve this question? Many of the terms have a # or a letter with a # or letter written just below it. I will use "sub" showing what is written that is lowered. It's like the opposite location from an exponent.
List the first six terms of the sequence defined recursively by (1) z(sub 1)=0, z(sub 2)=1, z (sub 3)=2, and (2) for m>=4, z(sub m)=z (sub m-1) + 2z(sub m-2) + 3z (sub m-3).
I sure hope that doesn't sound confusing. Any help you can give would be much appreciated. Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You are given the first 3 terms as system%28z%5B1%5D=0%2Cz%5B2%5D=1%2Cz%5B3%5D=2%29
and for the other terms you are given a recursive formula to calculate a term from the 3 previous terms:
for m%3E=4 , z%5Bm%5D=z%5B%28m-1%29%5D+%2B+2z%5B%28m-2%29%5D%2B+3z%5B%28m-3%29%5D .
Using that formula:
,
, and
.
So the first 6 terms are: 0, 1, 2, 4, 11, 25 .