Add to ORKGIn a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities
this paper, we study the modified Pell polynomials. We first give the proof of the generating functi...
In this paper, we first give the Pascal’s identity for Pellno-mial coefficients and then we show tha...
In this paper we prove several formulas for sums of squares of even Pell-Lucas numbers, sums of squa...
In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-know...
AMS Subject Classication: 05A19 Abstract. In a recent note, Santana and Diaz-Barrero proved a number...
In a recent note, Santana and Diaz–Barrero proved a number of sum identities involving the well–know...
Recently, Benjamin, Plott, and Sellers proved a variety of identities involving sums of Pell numbers...
We provide tiling proofs of several algebraic formulas for the Pell numbers of odd index, all of whi...
Abstract In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the...
Here we are proposing a generalized sum for Pell numbers. This sum contains four Pell numbers. By m...
In this study, Pell, Pell-Lucas and Modified Pell numbers are investigated. Using Binet formulas for...
This paper presents binomial theorems on combinatorial identities that are derived from the binomial...
Bodeen et al. recently considered a new combinatorial tiling problem wherein a “strip ” is tiled usi...
AbstractIn 1840, V.A. Lebesgue proved the following two series-product identities:∑n⩾0(−1;q)n(q)nq(n...
In this paper, we present a combinatorial proof for an identity involving the triangular numbers. Th...
this paper, we study the modified Pell polynomials. We first give the proof of the generating functi...
In this paper, we first give the Pascal’s identity for Pellno-mial coefficients and then we show tha...
In this paper we prove several formulas for sums of squares of even Pell-Lucas numbers, sums of squa...
In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-know...
AMS Subject Classication: 05A19 Abstract. In a recent note, Santana and Diaz-Barrero proved a number...
In a recent note, Santana and Diaz–Barrero proved a number of sum identities involving the well–know...
Recently, Benjamin, Plott, and Sellers proved a variety of identities involving sums of Pell numbers...
We provide tiling proofs of several algebraic formulas for the Pell numbers of odd index, all of whi...
Abstract In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the...
Here we are proposing a generalized sum for Pell numbers. This sum contains four Pell numbers. By m...
In this study, Pell, Pell-Lucas and Modified Pell numbers are investigated. Using Binet formulas for...
This paper presents binomial theorems on combinatorial identities that are derived from the binomial...
Bodeen et al. recently considered a new combinatorial tiling problem wherein a “strip ” is tiled usi...
AbstractIn 1840, V.A. Lebesgue proved the following two series-product identities:∑n⩾0(−1;q)n(q)nq(n...
In this paper, we present a combinatorial proof for an identity involving the triangular numbers. Th...
this paper, we study the modified Pell polynomials. We first give the proof of the generating functi...
In this paper, we first give the Pascal’s identity for Pellno-mial coefficients and then we show tha...
In this paper we prove several formulas for sums of squares of even Pell-Lucas numbers, sums of squa...