题目208：机器人行走

欧拉计划

Robot Walks

A robot moves in a series of one-fifth circular arcs (72°), with a free choice of a clockwise or an anticlockwise arc for each step, but no turning on the spot.

One of 70932 possible closed paths of 25 arcs starting northward is

Given that the robot starts facing North, how many journeys of 70 arcs in length can it take that return it, after the final arc, to its starting position?
(Any arc may be traversed multiple times.)

题目：

一个机器人以顺时针或逆时针的形式，每次都走五分之一圆弧（72°）的路线。如果回到它起点，则结束行走。

初始方向向北，总共走了 25 段圆弧的闭合路线有 70932 种，其中之一如下：

假定该机器人初始方向向北，请问，总共有多少种路线，可以使得该机器人经过 70 段圆弧的路径，又回到它的起点？

（每条圆弧都可被多次经过）