I don't understand this at all I have the solution but no idea.(adsbygoogle = window.adsbygoogle || []).push({});

I am suppose to find the recursion relation for consecutive 0 in a ternary string(String that contains only 0, 1 and 2)

So the solution I have is :

Strings starting with 1 = an(The n is the small n for recursion) - 1

Strings startring with 2 = an - 1

Strings starting with 01 = an - 2

Strings starting with 02 = an - 2

Strings starting with 00 = 3^n-2

So the relation is an = 2an-1 + 2an - 2 + 3^n-2 for n >= 3

So how did they get the relation?

Why an - 1? What is the length of the String they base their calculations on?

Example :

I take Strings starting with 1, I can have 10, 11, 12, why an - 1? and not an - 3, all 3 do not have consecutive 0s?

Or if I take the length of the String as 3, I can have 100, 110, 101, 102, 111.... so why -1? When I have so many other strings to minus off?

And also for 00,

Where did the 3^n come from?

This is so mind confusing.

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# Homework Help: Ternary String recursion relation

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