47 lines
1019 B
Markdown
47 lines
1019 B
Markdown
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---
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id: 5900f5091000cf542c51001b
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title: 'Problem 408: Admissible paths through a grid'
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challengeType: 5
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forumTopicId: 302076
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dashedName: problem-408-admissible-paths-through-a-grid
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---
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# --description--
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Let's call a lattice point (x, y) inadmissible if x, y and x + y are all positive perfect squares.
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For example, (9, 16) is inadmissible, while (0, 4), (3, 1) and (9, 4) are not.
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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.
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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.
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Find P(10 000 000) mod 1 000 000 007.
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# --hints--
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`euler408()` should return 299742733.
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```js
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assert.strictEqual(euler408(), 299742733);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler408() {
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return true;
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}
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euler408();
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```
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# --solutions--
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```js
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// solution required
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```
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