Balancing, pell and square triangular functions

On Pell, Pell-Lucas, and balancing numbers

In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.

Some New Properties of Balancing Numbers and Square Triangular Numbers

A number N is a square if it can be written as N = n2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing number if 8N2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers.

Dynamics of Triangular and Square Arrays

Firefighting on square, hexagonal, and triangular grids

In this paper, we consider the firefighter problem on a graph G = (V,E) that is either finite or infinite. Suppose that a fire breaks out at a given vertex v ∈ V . In each subsequent time unit, a firefighter protects one vertex which is not yet on fire, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefighter is to save as many vertices as...

Triangular approximations of fuzzy number with value and ambiguity functions