Beukers' integrals and Apéry's recurrences.
Bihyperbolic numbers of the Fibonacci type and their idempotent representation
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
Bijective proofs of parity theorems for partition statistics.
Binary BBP-formulae for logarithms and generalized Gaussian-Mersenne primes.
Binary linear forms over finite sets of integers
Binary relations on the power set of an -element set.
Binomial coefficient predictors.
Binomial sums via Bailey's cubic transformation
By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the -series, we examine a class of -series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
Binomials transformation formulae for scaled Fibonacci numbers
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
Blocks and progressions in subset sum sets
Bohr local properties of
Boundedness of oriented walks generated by substitutions
Let be a fixed point of a substitution on the alphabet and let and . We give a complete classification of the substitutions according to whether the sequence of matrices is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.
Bounding squares in second order recurrence sequences
Bounds for frequencies of residues of second-order recurrences modulo
The authors examine the frequency distribution of second-order recurrence sequences that are not -regular, for an odd prime , and apply their results to compute bounds for the frequencies of -singular elements of -regular second-order recurrences modulo powers of the prime . The authors’ results have application to the -stability of second-order recurrence sequences.
Bounds for linear recurrences with restricted coefficients.
Bounds for the 3x+1 problem using difference inequalities
Bounds for the counting function of the Jordan-Pólya numbers
A positive integer is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number .
Bounds for the Kolakoski sequence.
Bounds on ternary cyclotomic coefficients
Brownian motion and the generalized Catalan numbers.