# Project Euler Problem 445 - Retractions A (Sample Values)

#### Table of Contents

**Spoiler Alert!** This blog entry contains content that might help you solve problem 445 of Project Euler. Please don’t read any further if you have yet to attempt to solve the problem on your own. The information is intended for those who failed to solve the problem and are looking for hints. It is posted not before the problem has a hundred solvers already.

## Values for R(n)

n | R(n) |
---|---|

1 | 1 |

12 | 20 |

123 | 168 |

1234 | 1854 |

12345 | 9776 |

123456 | 7440 |

1234567 | 4416 |

12345678 | 5360 |

123456789 | 8320 |

## Values for ∑ R(c)

\[ \begin{equation} S(N) := \sum_{k=1}^{N-1}R\left({N \choose k} \right) \end{equation} \]

N | S(N) mod 1000000007 |
---|---|

10^{1} | 1118 |

10^{2} | 516982162 |

10^{3} | 853246560 |

10^{4} | 772758839 |

10^{5} | 628701600 |

## Archived Comments

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eulerian Jan 01, 2016 00:14:55 UTC