Binomial transform of the generalized third-order Jacobsthal sequence

2023

ARJOM

In this paper, we introduce and investigate the generalized Olivier sequences and we deal with, in detail, two special cases, namely, Olivier and Olivier-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. We also provide variousmatrices and identities associated with these sequences. Furthermore, we show that there are close relations between Olivier, Olivier-Lucas and adjusted Pell-Padovan, third order Lucas-Pell, third order Fibonacci-Pell, Pell-Perrin, Pell-Padovan numbers. Moreover, we give some identities and matrices related with thesesequences.

“…• For the application of generalized third-order Jacobsthal sequence to binomial transform, see [31].…”

Section: Discussionmentioning

confidence: 99%

Generalized Olivier Numbers

2023

ARJOM

“…• For the application of generalized third-order Jacobsthal sequence to binomial transform, see [45].…”

Section: Discussionmentioning

confidence: 99%

Generalized Friedrich Numbers

2023

JAMCS

In this paper, we define and investigate the generalized Friedrich sequences and we deal with, in detail, two special cases, namely, Friedrich and Friedrich-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relationsbetween Friedrich, Friedrich-Lucas and third order Jacobsthal, modified third-order Jacobsthal, third order Jacobsthal-Lucas numbers.

“…• For the application of generalized third-order Jacobsthal sequence to binomial transform, see [48].…”

Section: Discussionmentioning

confidence: 99%

A Study on Generalized Blaise Numbers

2023

AJARR

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 sequences. Furthermore, we show that there are close relations between Blaise, Blaise-Lucas and Jacobsthal-Padovan, Jacobsthal-Perrin, adjusted Jacobsthal-Padovan, modified Jacobsthal-Padovan numbers. Moreover, we give some identities and matrices related with these sequences.