(Subscript[Φ, em,d_]):=(Subscript[Φ, em,d])=(Subscript[𝕆, AR,{x,y},{1}])[(Subscript[𝒜, 0])[(Subscript[AWExp, d])[ι[φ[d]]]/.aw_AW:>(Subscript[AW, 1])@@(aw/.{1->x,2->y})]]

F[0]=1; F[1]=1; F[n_]:=F[n-1]+F[n-2]

Table[F[n],{n,0,10}]

Table[F[n],{n,0,20}]

Timing@Table[F[n],{n,0,30}]

G[0]=1; G[1]=1; G[n_]:=(G[n]=G[n-1]+G[n-2])

Timing@Table[G[n],{n,0,30}]

Timing@Table[G[n],{n,0,100}]

?F

?G

a=Date[]

a

a

b:=Date[]

b

b