What are pell numbers?

Pell numbers are like steps you take when climbing a special kind of staircase.

Imagine you're playing a game where you can climb either 1 step or 2 steps at a time. The pell numbers count how many different ways you can reach each step.

Let’s say the first step is number 1. You can only get there by taking one step. So that’s our first pell number: 1.

Now for step 2, you can either take two single steps or one double step. That makes 2 ways to reach step 2, so that’s our second pell number: 2.

For step 3, think about how many ways you could have gotten there before. If you were on step 1 and took one more step, or you were on step 2 and took one more step. So we add the previous two numbers together to get the next one:

1 + 2 = 3.

So the pell number for step 3 is 3, and this pattern keeps going, each new pell number is just the sum of the last two! That’s what makes them special. It’s like a friendly rule that helps you figure out how many ways there are to climb up, one step at a time.