A).$2^{n}+1$
$n=0,2^{0}+1=1+1=2$
$n=1,2^{1}+1=2+1=3$
$n=2,2^{2}+1=4+1=5$
$n=3,2^{3}+1=8+1=9$
B).$(n+1)^{n+1}$
$n=0,(0+1)^{0+1}=1^{1}=1$
$n=1,(1+1)^{1+1}=2^{2}=4$
$n=2,(2+1)^{2+1}=3^{3}=27$
$n=3,(3+1)^{3+1}=4^{4}=64$
C).$⌊n/2⌋$
$n=0,⌊0/2⌋=0$
$n=1,⌊1/2⌋=0$
$n=2,⌊2/2⌋=1$
$n=3,⌊3/2⌋=1$
D).$⌊n/2⌋+⌈n/2⌉$
$n=0,⌊0/2⌋+⌈0/2⌉=0+0=0$
$n=1,⌊1/2⌋+⌈1/2⌉=0+1=1$
$n=2,⌊2/2⌋+⌈2/2⌉=1+1=2$
$n=3,⌊3/2⌋+⌈3/2⌉=1+2=3$