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- W3102455900 abstract "Let $V_{n}$ denote the third order linear recursive sequence defined by the initial values $V_{0}$, $V_{1}$ and $V_{2}$ and the recursion $V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}$ if $ngeq 3$, where $r$, $s$, and $t$ are real constants. The ${V_{n}}_{ngeq0}$ are generalized Tribonacci numbers and reduce to the usual Tribonacci numbers when $r=s=t=1$ and to the $3$-bonacci numbers when $r=s=1$ and $t=0$. In this study, we introduced a quaternion sequence which has not been introduced before. We show that the new quaternion sequence that we introduced includes the previously introduced Tribonacci, Padovan, Narayana and Third order Jacobsthal quaternion sequences. We obtained the Binet formula, summation formula and the norm value for this new quaternion sequence." @default.
- W3102455900 created "2020-11-23" @default.
- W3102455900 creator A5080157107 @default.
- W3102455900 date "2017-11-16" @default.
- W3102455900 modified "2023-09-23" @default.
- W3102455900 title "On a Generalization for Tribonacci Quaternions" @default.
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- W3102455900 doi "https://doi.org/10.1007/s00009-017-1042-3" @default.
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