---
id: 5900f5091000cf542c51001b
title: 'Problem 408: Admissible paths through a grid'
challengeType: 5
forumTopicId: 302076
dashedName: 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 ($x_1$, $y_1$) to point ($x_2$, $y_2$) 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 $P(5) = 252$, $P(16) = 596\\,994\\,440$ and $P(1\\,000)\bmod 1\\,000\\,000\\,007 = 341\\,920\\,854$.

Find $P(10\\,000\\,000)\bmod 1\\,000\\,000\\,007$.

# --hints--

`admissiblePaths()` should return `299742733`.

```js
assert.strictEqual(admissiblePaths(), 299742733);
```

# --seed--

## --seed-contents--

```js
function admissiblePaths() {

  return true;
}

admissiblePaths();
```

# --solutions--

```js
// solution required
```