General form of some rational recursive sequences

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

P - Recursive Integer Sequences and Automata Theory

of the Dissertation P-Recursive Integer Sequences and Automata Theory by Scott Michael Garrabrant Doctor of Philosophy in Mathematics University of California, Los Angeles, 2015 Professor Igor Pak, Chair An integer sequence {an} is called polynomially recursive, or P-recursive, if it satisfies a nontrivial linear recurrence relation of the form q0(n)an + q1(n)an−1 + . . . + qk(n)an−k = 0 , for ...

On a (2,2)-rational Recursive Sequence

We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+ βyn)/(1 + yn−1) when the parameters α < 0 and β ∈ R. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1 = (a+ byn)/(A+Byn−1), when th...

RATIONAL CHARACTER TABLE OF SOME FINITE GROUPS

The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...

QArith: Coq Formalisation of Lazy Rational Arithmetic

In this paper we present the Coq formalisation of the QArith library which is an implementation of rational numbers as binary sequences for both lazy and strict computation. We use the representation also known as the Stern-Brocot representation for rational numbers. This formalisation uses advanced machinery of the Coq theorem prover and applies recent developments in formalising general recur...