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An Introduction to Completeness of Positive Linear Recurrence Sequences
Elżbieta Bołdyriew, John Haviland, Phúc Lâm +3
A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneous linear recurrence relation with positive coefficients and a particular set of initial conditions…
Completeness of Positive Linear Recurrence Sequences
Elżbieta Bołdyriew, John Haviland, Phúc Lâm +3
A sequence of positive integers is complete if every positive integer is a sum of distinct terms. A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneou…
Extending Zeckendorf's Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation
Elżbieta Bołdyriew, Anna Cusenza, Linglong Dai +16
Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from . This has been gene…
Counting on Euler and Bernoulli Number Identities
Arthur T. Benjamin, John Lentfer, Thomas C. Martinez
While there are many identities involving the Euler and Bernoulli numbers, they are usually proved analytically or inductively. We prove two identities involving Euler and Bernoull…