Consider a grid of black and white squares with 3 rows and n columns. If there is a non-empty sequence of white squares s_{1}, \ldots, s_{m} such that s_{1} is in the top row and s_{m} is in the bottom row and consecutive squares in the sequence share an edge, then we say that the grid percolates. Let T_{n} be the number of grids which do not percolate. There exists constants a, b such that \frac{T_{n}}{a b^{n}} \rightarrow 1 as n \rightarrow \infty. Then b is expressible as (x+\sqrt{y}) / z for squarefree y and coprime x, z. Find x+y+z.