Cells counting problem [closed]

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There is a 3D grid with cells for which we define its value (0 or 1) as F(i,j,k)=F(开发者_StackOverflow社区i-1,j,k) XOR F(i,j-1,k) XOR F(i,j,k-1), base cases are F(0,0,0)=1 and F(x,y,z)=0 for x < 0 or y < 0 or z < 0 (if at least one parameter is negative). We want to count amount of cells with F()=1 in the cube with corners (0,0,0) and (N, M, K). Dimensions are about 2^30.

I'm looking for the fast approach on this problem.