Triangle time (just without geo)

Consider the triangle below. (Every number is the sum of the numbers above it. If at least one of the numbers above it is missing, then assume that there is a 0.) 1 1 1 1 1 2 3 2 1 1 3 6 7 6 3 1 1 \\ 1 \ 1 \ 1 \\ 1 \ 2 \ 3 \ 2 \ 1 \\ 1 \ 3 \ 6 \ 7 \ 6 \ 3 \ 1 \\ \dots

Find the number of rows untill the 2016th row, which contain at least one even number.


The answer is 2014.

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