In this paper, we introduce and investigate the generalized Blaise sequences and we deal with, in detail, two special cases, namely, Blaise and Blaise-Lucas sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequenc...
Open access
Research Article10.9734/ajarr/2023/v17i1463
In this paper, closed forms of the sum formulas \(\sum{^n_k{_=}{_0}}x^kW{^2_m{_k}_+{_j}}\) for generalized p-Oresme numbers are presented. As special cases, we give sum formulas of Modified p-Oresme, p-Oresme-Lucas and p-Oresme numbers. We present the proofs to indicate how these...
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Research Article10.9734/ajarr/2022/v16i130444
In this paper, we define the binomial transform of the generalized fifth order Pell sequence and as special cases, the binomial transform of the fifth order Pell and fifth order Pell-Lucas sequences will be introduced. We investigate their properties in details. We present Binet’...
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Research Article10.9734/ajarr/2021/v15i930423
In this study, we define the binomial transform of the generalized fourth order Pell sequence and as special cases, the binomial transform of the fourth order Pell and fourth order Pell-Lucas sequences will be introduced. We investigate their properties in details.
Open access
Research Article10.9734/acri/2021/v21i630250
In this paper, we introduce the generalized p-Oresme sequences and we deal with, in detail, three special cases which we call them modified p-Oresme, p-Oresme-Lucas and p-Oresme sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formu...
Open access
Research Article10.9734/ajarr/2021/v15i730410
In this paper, closed forms of the summation formulas ∑nk=0 xkWmk+j for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how the...
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Research Article10.9734/acri/2021/v21i330235
In this paper, we investigate the recurrence properties of the generalized Hexanacci sequence under the mild assumption that the roots of the corresponding characerteristic polynomial are all distinct, and present how the generalized Hexanacci sequence at negative indices can be...
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Research Article10.9734/ajarr/2021/v15i230370
In this paper, closed forms of the summation formulas for generalized Hexanacci numbers are presented. As special cases, we give summation formulas of Hexanacci, Hexanacci-Lucas, sixth order Pell, sixth order Pell-Lucas, sixth order Jacobsthal, sixth order Jacobsthal-Lucas number...
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Research Article10.9734/ajarr/2020/v14i230329
In this paper, we introduce the generalized 6-primes sequence and we deal with, in detail, three special cases which we call them 6-primes, Lucas 6-primes and modified 6-primes sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formul...
Open access
Research Article10.9734/acri/2020/v20i630199
In this paper, we investigate the generalized Pell-Padovan sequences and we deal with, in detail, four special cases, namely, Pell-Padovan, Pell-Perrin, third order Fibonacci-Pell and third order Lucas-Pell sequences. We present Binet’s formulas, generating functions, Simson form...
Open access
Research Article10.9734/ajarr/2020/v11i230259
In this paper, closed forms of the sum formulas Σn k=0 xkW2 k ; Σn k=0 xk Σ Wk+1Wk and n k=0 xkWk+2Wk for the squares of generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin numbers and the oth...
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Research Article10.9734/acri/2020/v20i430187
In this paper, we introduce the generalized 2-primes sequences and we deal with, in detail, three special cases which we call them 2-primes, Lucas 2-primes and modified 2-primes sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formu...
Open access
Research Article10.9734/ajarr/2020/v9i230217
In this paper, closed forms of the summation formulas for generalized Tetranacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, fourth order...
Open access
Research Article10.9734/ajarr/2019/v7i230170
In this paper, we investigate the generalized third order Pell sequences and we deal with, in detail, three special cases which we call them third order Pell, third order Pell-Lucas and modified third order Pell sequences. We present Binet’s formulas, generating functions, Simson...
Open access
Research Article10.9734/ajarr/2019/v6i130144