Notation involving recursive function

sequences-and-series recurrence-relations

As you said, for $n = 1$ you have $K_1=1$. Similarly, $K_2=2$ and $K_3=3$.

Than little number is called a subscript and is often used to designate the $n-th$ item in a sequence. The other equation tells you how to continue the sequence. Let's practice two more:

$$ K_4 = K_3 + 2K_2 + 3K_1 = 3+2\cdot 2 + 3\cdot 1 = 10 \\ K_5 = K_4 + 2K_3 + 3K_2 = 10 +2\cdot 3 + 3\cdot 2 = 24 \\ $$ By the way, for large values of $n$, $K_n$ is about $0.29 \cdot (2.3744)^n$.

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