---
id: 5900f53c1000cf542c51004e
title: 'Problem 463: A weird recurrence relation'
challengeType: 5
forumTopicId: 302138
dashedName: problem-463-a-weird-recurrence-relation
---

# --description--

The function $f$ is defined for all positive integers as follows:

$f(1)=1$

$f(3)=3$

$f(2n)=f(n)$

$f(4n + 1)=2f(2n + 1) - f(n)$

$f(4n + 3)=3f(2n + 1) - 2f(n)$

The function $S(n)$ is defined as $\\sum\_{i=1}^{n}f(i)$. $S(8)=22$ and $S(100)=3604$. Find $S(3^{37})$. Give the last 9 digits of your answer.

# --hints--

`euler463()` should return 808981553.

```js
assert.strictEqual(euler463(), 808981553);
```

# --seed--

## --seed-contents--

```js
function euler463() {

  return true;
}

euler463();
```

# --solutions--

```js
// solution required
```