Problem $1$: Recursion and Tail Recursion

In class for the second lecture we practiced recursion on this fuction:

$(0$n$02$n$+$h$($n$1)+$h$($n$2)$ o$.$w$.$

$(1)$

$(2)$

h$($n$)=$

If we tried our first technique to implement tail recursion, we$$d have this:

htr$($n$,$ acc$0,$ acc$1)$ The first ten values are:

$1$h$(0)=1$;htr$(0)=1$

$2$h$(1)=4$;htr$(1)=4$

$3$h$(2)=9$;htr$(2)=9$

$4$h$(3)=19$; htr$(3)=19$

$5$h$(4)=36$; htr$(4)=40$

$6$h$(5)=65$; htr$(5)=79$

$7$h$(6)=113$; htr$(6)=153$

$8$h$(7)=192$; htr$(7)=288$

$9$h$(8)=321$; htr$(8)=533$

$10$h$(9)=531$; htr$(9)=971$

$=$

$($

$[$acc$0,$ acc$1][$n$]$

htr$($n $1,$ acc$1,2$n $+$ acc$0+$ acc$1)$

n $2$ o$.$w$.$