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User:Spundun/Math

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For any new level added we need to calculate the # of new upright triangles and new inverted triangles.

Upright Triangles

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For any level , The # of new upright triangles is

So the cumulative upright triangles are

Inverted Triangles

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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)