Pell and Pell–Lucas Numbers

On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers

“…In this work, we investigate summation formulas of generalized Fibonacci and Gaussian generalized Fibonacci numbers. Some summing formulas of the Pell and Pell-Lucas numbers are well known and given in [6], [7], see also [8]. For linear sums of Fibonacci, Tribonacci, Tetranacci, Pentanacci and Hexanacci numbers, see [9], [10], [11], [12], [13], and [14] respectively.…”

On a four-parameter generalization of some special sequences

“…Finally, if a type F tilingof an (n + 1)-board ends with a k-rectangle, then we remove this piece to create a tiling enumerated by F i r,1 (k, n − k). Two known identities to the Fibonacci and Pell numbers can be obtained from (8): 3F n = F n+2 +F n−2 (see [5]) and 6P n = P n+2 +P n−2 , (see [23]), ∀n ≥ 2.…”

On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

“…Some summing formulas of the Pell and Pell-Lucas numbers are well known and given in [1,2], see also [3]. For linear sums of Tribonacci and Tetranacci and Pentanacci numbers, see [4], [5,6] and [7], respectively.…”