New families of Horadam numbers associated with finite operators and their applications
Can Kızılateş
Abstract
In this paper, by applying finite operator to the Horadam sequence, we define the Horadam finite operator sequences. We not only give some special cases of this new sequences but also investigate some properties of our new sequences such as recurrent relation, Binet‐like formula, summation formula, and generating function, respectively. We also present closed formula for the Horadam finite operator numbers and their special cases in terms of tridiagonal determinants. Moreover, by using the tridiagonal determinant, we once again verify the recurrence relation of the Horadam finite operator numbers.
Topics & Concepts
MathematicsTridiagonal matrixOperator (biology)Sequence (biology)Recurrence relationRelation (database)Algebra over a fieldPure mathematicsBitwise operationFunction (biology)Generating functionDiscrete mathematicsApplied mathematicsMathematical analysisEigenvalues and eigenvectorsComputer scienceGeneticsQuantum mechanicsChemistryDatabaseTranscription factorProgramming languageEvolutionary biologyBiochemistryRepressorBiologyGenePhysicsAdvanced Mathematical Theories and ApplicationsGraph Labeling and Dimension Problems