New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers

On Quaternions with Higher Order Jacobsthal Numbers Components

“…Many scientists have been interested in number sequences for many years, as they find application in nature and in many sciences [11][12][13][14][15]. Many generalizations of number sequences were then described and studied [15][16][17][18]. One of the most well-known number sequences is the Jacobsthal numbers [19][20][21][22][23].…”

Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers

“…As polynomial extensions of the Fibonacci/Lucas numbers, the Pell/Lucas polynomials have many remarkable properties and wide applications in mathematics, physics, and computer sciences (see Koshy [1,2] and Grimaldi [3]). There exist numerous summation formulae involving Fibonacci/Lucas numbers [4][5][6][7][8] and the Pell/Lucas polynomials [9][10][11][12][13][14][15]. Motivated by a beautiful formula (see Corollary 3) due to Ohtsuka [16], we shall investigate in this paper further summation formulae involving inverse central binomial coefficients and Pell/Lucas polynomials, as well as their applications to identities concerning Fibonacci/Lucas numbers.…”

On hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions

“…Of course, the Fibonacci numbers are the best known of the sequences of numbers. Many generalizations of number sequences were then described and studied [4,5,12,15,19]. One of these generalizations is the Jacobsthal numbers [7,8,14,15,17,19].…”