for the rest of the array we will rely on the previous entries to compute new ones
for ( N = 1 ; N <= 20 ; N ++ ) printf ( " Maximum ▁ Number ▁ of ▁ A ' s ▁ with ▁ % d ▁ keystrokes ▁ is ▁ % d STRNEWLINE " , N , findoptimal ( N ) ) ; }