Originally Posted by
Plato As stated this is what we let $\mathcal{T}_n$ be the collection of ternary strings of length $n$ that contain two consecutive 0s".
We denote the number of elements in $\mathcal{T}_n$ by ${t}_n$.
$\mathcal{T}_1=\emptyset$ so $t_1=0$
$\mathcal{T}_2=\{00\}$ so $t_2=1$
$\mathcal{T}_3=\{~000,~100,~200,001,002\}$ so $t_3=4$
Be sure that I constructed those correctly & that I counted all.
How was $\mathcal{T}_3$ constructed using $\mathcal{T}_1,~\&~\mathcal{T}_2~?$
What does $\mathcal{T}_4$ look like and how is it constructed?