Stairs problem (recurrence)

Consider a staircase with n stairs which one can clim by 2 stairs or by 3 stairs at each step. e.g. a staircase with n=9 stairs can be climbed in exactly 5 ways.

Write a recurrence relation for the number of ways to ascend this staircase.

I worked out the values for [Consider a staircase with n stairs which one can clim by 2 stairs or by 3 stairs at each step. e.g. a staircase with n=9 stairs can be climbed in exactly 5 ways.

Write a recurrence relation for the number of ways to ascend this staircase.

I worked out the values for up to 9:

which gave me but I think this is wrong.

Please double-check my values for /help me solve this!