freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-463-a-weird-recurrence-relation.md

id, title, challengeType, forumTopicId, dashedName

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

--description--

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

$$\begin{align} & f(1) = 1 \\ & f(3) = 3 \\ & f(2n) = f(n) \\ & f(4n + 1) = 2f(2n + 1) - f(n) \\ & f(4n + 3) = 3f(2n + 1) - 2f(n) \end{align}$$

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--

weirdRecurrenceRelation() should return 808981553.

assert.strictEqual(weirdRecurrenceRelation(), 808981553);

--seed--

--seed-contents--

function weirdRecurrenceRelation() {

  return true;
}

weirdRecurrenceRelation();

--solutions--

// solution required