For any new level added we need to calculate the # of new upright triangles and new inverted triangles.
For any level
, The # of new upright triangles is
So the cumulative upright triangles are
For any level
, the biggest inverted triangle will have sides
For both
... and so on.
The # of inverted triangles over the level
of side
will be
So the total # of inverted triangles introduced by a level
will be
is a function of
so we can write it as
So total accumulated inverted triangles over all the levels is
Expressing
in terms of
if
is even
if
is odd
an even and odd pair would have the same
So the summation can be written as
plus (if
is even)
plus (if
is even)
plus (if
is even)
plus (if
is even)
plus (if
is even)
plus (if
is even)
plus (if
is even)
plus (if
is even)