Combinatorial interpretations of a generalization of the Genocchi numbers.
The purpose of this paper is to prove that the common terms of linear recurrences and have at most common terms if , and have at most three common terms if where and are fixed positive integers and is a prime, such that neither nor is perfect square, further are nonzero integers satisfying the equations and .
We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied