I would like to ask for details to fully understand the calculation of the convolution with the two discrete signals below
$$\begin{aligned} x[n] &= δ[n+1] + 2δ[n] + 2δ[n−2] + 3δ[n−3]\\ h[n] &= δ[n] + δ[n-1] \end{aligned}$$
By applying the staircase method I found the following
$$y[n] = [ 1 , 3, 2, 2, 5, 3 ]$$
but I am not sure I am right. I would be very grateful if anyone could clarify this.