# Pascal Pyramid

Pascal's Triangle is the following pattern of numbers

 1 2 3 4  1 1 2 1 1 3 3 1 1 4 6 4 1 

Now, consider the Pascal's Pyramid, an extension of Pascal's Triangle. Instead of adding two numbers in the row above, Pascal's Pyramid adds 3 adjacent numbers from the layer above. When viewing from top,

Layer 0 :

 1 1 

Layer 1 :

 1 2 1 1 1 

Layer 2 :

 1 2 3 1 2 1 2 2 1 

What is the sum of numbers in layer 8?

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