What is the sum of the first few centered hexagonal numbers, given the sequence 1, 7, 19, 37, ...?

Step 1: Identify the sequence being added.
The question asks to add up the sequence $1, 7, 19, 37, \dots$. These numbers are known as centered hexagonal numbers.
The formula for the $n$-th centered hexagonal number is $CH_n = 3n^2 - 3n + 1$.
Let's verify the first few terms:
For $n=1$: $CH_1 = 3(1)^2 - 3(1) + 1 = 3 - 3 + 1 = 1$.
For $n=2$: $CH_2 = 3(2)^2 - 3(2) + 1 = 12 - 6