yaworsw/euler-manager

---
:id: 312
:name: Cyclic paths on Sierpiński graphs
:url: https://projecteuler.net/problem=312
:content: "- A **Sierpiński graph** of order-1 (<var>S</var><sub>1</sub>) is an equilateral
  triangle.  \n- <var>S</var><sub><var>n</var>+1</sub> is obtained from <var>S</var><sub><var>n</var></sub>
  by positioning three copies of <var>S</var><sub><var>n</var></sub> so that every
  pair of copies has one common corner.\n\n ![p312_sierpinskyAt.gif]({{ images_dir
  }}/p312_sierpinskyAt.gif)\n\nLet C(<var>n</var>) be the number of cycles that pass
  exactly once through all the vertices of <var>S</var><sub><var>n</var></sub>.  \nFor
  example, C(3) = 8 because eight such cycles can be drawn on <var>S</var><sub>3</sub>,
  as shown below:\n\n ![p312_sierpinsky8t.gif]({{ images_dir }}/p312_sierpinsky8t.gif)\n\nIt
  can also be verified that :  \nC(1) = C(2) = 1  \nC(5) = 71328803586048  \nC(10
  000) mod 10<sup>8</sup> = 37652224  \nC(10 000) mod 13<sup>8</sup> = 617720485\n\nFind
  C(C(C(10 000))) mod 13<sup>8</sup>.\n\n"