### Abstract

We evaluate the number u(n) of length-n finite sequences (ak)1≤k≤n of natural numbers that satisfy the inequality ak ≤ k^{2} for all k. We thus determine two recurrence relations for u(n) by two different methods, and we give an explicit expression in closed form for it.

Original language | English (US) |
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Article number | 15.1.8 |

Journal | Journal of Integer Sequences |

Volume | 18 |

Issue number | 1 |

State | Published - Jan 13 2015 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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## Cite this

Haddad, L., & Helou, C. (2015). Finite sequences dominated by the squares.

*Journal of Integer Sequences*,*18*(1), [15.1.8].