## Challenge 327: Nic's Squares

Nic is investigating a family of number diagrams.

Here are the first few:

1 |

1 |
1 |

1 |
2 |

1 |
1 |
1 |

1 |
2 |
2 |

1 |
2 |
3 |

** **

1 |
1 |
1 |
1 |

1 |
2 |
2 |
2 |

1 |
2 |
3 |
3 |

1 |
2 |
3 |
4 |

** **

Nic calculates the total of the numbers in each number square, forming a sequence that starts

1, 5, 14, 30…

What will the 10^{th} term in the sequence be?

What about the 100^{th} term? Or the n^{th} term?

Bonus question: What has this got to do with square numbers? How is this connected to the diagrams?