On a New One Parameter Generalization of Pell Numbers

Abstract

In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers. Moreover, we give a graph interpretation of these numbers.

On Some Combinatorial Properties of P (r, n)-Pell Quaternions

“…In the literature, there are some generalizations of the Pell numbers, see [2,3,10,11]. In [1], a one parameter generalization of the Pell numbers was investigated. We recall this generalization.…”

“…In [1], it was proved that the r-Pell numbers can be used for counting the independent sets of special classes of graphs.…”

“…The quaternion multiplication is also defined analogously to the complex numbers multiplication using the rules (1) and (2). Unlike the multiplication of real numbers and complex numbers the multiplication of quaternions is not commutative.…”

ON GENERALIZED (k, r) – GAUSS PELL NUMBERS

“…Some of these are [1][2][3][4][5][6][7][8][9][10]. We see some generalizations of Pell numbers in [11][12][13][14][15][16]. Also, we see some works on generalized Gauss numbers in [17][18][19].…”