English

Identities and congruences for a new sequence

Number Theory 2010-12-21 v1

Abstract

Let [x][x] be the greatest integer not exceeding xx. In the paper we introduce the sequence {Un}\{U_n\} given by U0=1U_0=1 and Un=2k=1[n/2](n2k)Un2k(n1)U_n=-2\sum_{k=1}^{[n/2]}\binom n{2k}U_{n-2k}\quad(n\ge 1), and establish many recursive formulas and congruences involving {Un}\{U_n\}.

Keywords

Cite

@article{arxiv.1012.4034,
  title  = {Identities and congruences for a new sequence},
  author = {Zhi-Hong Sun},
  journal= {arXiv preprint arXiv:1012.4034},
  year   = {2010}
}

Comments

18 pages

R2 v1 2026-06-21T17:00:52.374Z