Problem $3$: Pyramids of Egypt

This recursion is an old mathematical way to build a pyramid of numbers.

m$([$x$])=[]$

m$([$x$,$ y$])=[[$x $+$ y$]]$

m$([$x$0,$ x$1,$ x$2,...,$ xn$]=$ m$([$x$0+$ x$1,$ x$1+$ x$2,+,$ xn$1+$ xn$])+[[$x$0+$ x$1,$ x$1+$ x$2,,$ xn$1+$ xn$]]$

The code:

x $=[[1,2,3,4,5],[1],[3,4],[5,10,22],[1,2,3,4,5,6]]$

for i in x:

print$($m$($i$))$

produces:

$[[48],[20,28],[8,12,16],[3,5,7,9]]$

$[]$

$[[7]]$

$[[47],[15,32]]$

$[[112],[48,64],[20,28,36],[8,12,16,20],[3,5,7,9,11]]$

Observe, for example, $[1,2,3,4,5].$ This becomes the base: $[1+2,2+3,3+4,4+5].$ Then this becomes the first story $[3+5,5+7,7+9].$

Deliverables Programming Problem $3$

$$Complete the function m

Code should begin with:

def m$($lst$)$:

$...$

$($DONT USE ANY AI TO SOLVE THIS PROBLEM$)$