freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-408-admissible-paths-through-a-grid.english.md

id, challengeType, title

id	challengeType	title
5900f5091000cf542c51001b	5	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.

Instructions

Tests

tests:
  - text: <code>euler408()</code> should return 299742733.
    testString: 'assert.strictEqual(euler408(), 299742733, ''<code>euler408()</code> should return 299742733.'');'

Challenge Seed

function euler408() {
  // Good luck!
  return true;
}

euler408();

Solution

// solution required