1019 B

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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

1019 B Raw Blame History