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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