---
id: 5900f4a51000cf542c50ffb7
title: 'Problem 312: Cyclic paths on Sierpiński graphs'
challengeType: 5
forumTopicId: 301968
dashedName: problem-312-cyclic-paths-on-sierpiski-graphs
---
# --description--
- A Sierpiński graph of order-1 ($S_1$) is an equilateral triangle.
- $S_{n + 1}$ is obtained from $S_n$ by positioning three copies of $S_n$ so that every pair of copies has one common corner.
Let $C(n)$ be the number of cycles that pass exactly once through all the vertices of $S_n$. For example, $C(3) = 8$ because eight such cycles can be drawn on $S_3$, as shown below:
It can also be verified that:
$$\begin{align}
& C(1) = C(2) = 1 \\\\
& C(5) = 71\\,328\\,803\\,586\\,048 \\\\
& C(10 000)\bmod {10}^8 = 37\\,652\\,224 \\\\
& C(10 000)\bmod {13}^8 = 617\\,720\\,485 \\\\
\end{align}$$
Find $C(C(C(10\\,000)))\bmod {13}^8$.
# --hints--
`pathsOnSierpinskiGraphs()` should return `324681947`.
```js
assert.strictEqual(pathsOnSierpinskiGraphs(), 324681947);
```
# --seed--
## --seed-contents--
```js
function pathsOnSierpinskiGraphs() {
return true;
}
pathsOnSierpinskiGraphs();
```
# --solutions--
```js
// solution required
```