On the recursive sequence xn+1=

On the Rational Recursive Sequence xn + 1 = (A + sum k i = 0 alpha i xn - i)/(B + sum k i = 0 beta i xn - i)

Several Results on Sequences Which Are Similar to the Positive Integers

Sequence of positive integers {xn}n≥1 is called similar to N with respect to a given property A if for every n ≥ 1 the numbers xn and n are in the same class of equivalence with respect to A (xn ∼ n(prop A)). If x1 = a(> 1) ∼ 1(prop A) and xn > xn−1 with the condition that xn is the nearest to xn−1 number such that xn ∼ n(prop A), then the sequence {xn} is called minimal recursive with the firs...

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

Almost Sure Convergence Rates for the Estimation of a Covariance Operator for Negatively Associated Samples

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...

On the Recursive Sequence xn 1 A x p n − 1 / x q n

On the Periodicity of Certain Recursive Sequences

In 2000, Viswanath showed that random Fibonacci sequences grow exponentially and calculated the rate at which they grow assuming the coin flipped was fair. In this paper, we explore the Fibonacci sequences generated by finite, repeating sequences of pluses and minuses. The main results of this paper will be to show the necessary conditions for a sequence to be periodic, as well as to show all t...