A case study in meta-automation: automatic generation of congruence automata for combinatorial sequences

DOI10.1080/10236198.2013.876422zbMath1358.68175arXiv1311.4776OpenAlexW2011123341MaRDI QIDQ5168653

Doron Zeilberger, Eric S. Rowland

Publication date: 18 July 2014

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.4776

zbMATH Keywords

finite automatonautomatic sequenceconstant termsequences modulo \(m\)

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Formal languages and automata (68Q45) Congruences; primitive roots; residue systems (11A07) Special sequences and polynomials (11B83) Automata sequences (11B85) Sequences (mod (m)) (11B50) General topics in the theory of algorithms (68W01)

Related Items (8)

On the period mod $m$ of polynomially-recursive sequences: a case study ⋮ On congruence schemes for constant terms and their applications ⋮ Generalized Lucas congruences and linear \(p\)-schemes ⋮ Congruence properties of combinatorial sequences via walnut and the Rowland-Yassawi-Zeilberger automaton ⋮ Gessel-Lucas congruences for sporadic sequences ⋮ \(p\)-adic asymptotic properties of constant-recursive sequences ⋮ Automated discovery and proof of congruence theorems for partial sums of combinatorial sequences ⋮ Automatic congruences for diagonals of rational functions

Uses Software

• Maple
• OEIS
• AutoSquared
• CatalanCC
• MotzkinCC
• DelannoyLS

Cites Work

• Automatic congruences for diagonals of rational functions
• A Riccati differential equation and free subgroup numbers for lifts of \(\mathrm{PSL}_2(\mathbb Z)\) modulo prime powers

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