Sums and spectral norms of all almost balancing numbers

Abstract

In this work, we derive some algebraic relations on sums of all almost balancing numbers of first and second type. We also deduce some formulas on sums of Pell, Pell–Lucas and balancing numbers in terms of all almost balancing numbers of first and second type. Further, we formulate the eigenvalues and spectral norms of circulant matrices of all almost balancing numbers of first and second type.