How many orbitals are in the n equals 4 shell

For the Principal quantum number n = 4, we have the 4th shell of which
the Orbital quantum numbers are l = 0, 1, 2, and 3,
n=4, l=0 is called 4s ; n=4, l=1 is called 4p ; n=4, l=2 is called 4d ; n=4, l=3 is called 4f
When l=0, magnetic quantum number is m(l)= 0 ; 4s has one orbital
When l=1, magnetic quantum numbers are m(l)= -1, 0, +1 ; 4p has 3 orbitals
When l=2, magnetic quantum numbers are m(l)= -2, -1, 0, +1, +2 ; 4d has 5 orbitals
When l=3, magnetic quantum numbers are m(l)= -3, -2, -1, 0, +1, +2, +3 ; 4f has 7 orbitals
So there are in all 1+3+5+7=16 orbitals
Each m(l) value has 2 m(s) values, +1/2 and -1/2, called magnetic spin quantum numbers and
each orbital can accommodate 2 electrons with m(s)=+1/2 and -1/2
Thus n=4 shell can accommodate 32 electrons maximum.