# Problem 408: Admissible paths through a grid
Let's call a lattice point (x, y) inadmissible if x, y and x + y are all
positive perfect squares. For example, (9, 16) is inadmissible, while
(0, 4), (3, 1) and (9, 4) are not. Consider a path from point (x1, y1)
to point (x2, y2) using only unit steps north or east. Let's call such a
path admissible if none of its intermediate points are inadmissible. Let
P(n) be the number of admissible paths from (0, 0) to (n, n). It can be
verified that P(5) = 252, P(16) = 596994440 and P(1000) mod
1 000 000 007 = 341920854. Find P(10 000 000) mod 1 000 000 007.