1019 B
1019 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5091000cf542c51001b | Problem 408: Admissible paths through a grid | 5 | 302076 | problem-408-admissible-paths-through-a-grid |
--description--
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.
--hints--
euler408()
should return 299742733.
assert.strictEqual(euler408(), 299742733);
--seed--
--seed-contents--
function euler408() {
return true;
}
euler408();
--solutions--
// solution required