Geodesic
On a quaternionic sequence with Vietoris' numbers
Filomat, Tome 35 (2021) no. 4, p. 1065

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DOI

Special integers sequences have been the center of attention for many researchers, as well as the sequences of quaternions where its components are the elements of these sequences. Motivated by a rational sequence, we consider the quaternions with components Vietoris' numbers and investigate some of its properties. For this sequence a two and three term recurrence relation is established, as well as a Binet's type formula. Moreover the generating function for this sequence is introduced and also the determinant of some tridiagonal matrices are used in order to find elements of this sequence
DOI : 10.2298/FIL2104065C
Classification : 11R52, 05A10, 11B37, 05A15
Keywords: Binet’s formula, Catalan’s identity, Generating function, Quaternions, Recurrence relation, Tridiagonal matrix, Vietoris’ number sequence 
P Catarino; R De Almeida. On a quaternionic sequence with Vietoris' numbers. Filomat, Tome 35 (2021) no. 4, p. 1065 . doi: 10.2298/FIL2104065C
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     author = {P Catarino and R De Almeida},
     title = {On a quaternionic sequence with {Vietoris'} numbers},
     journal = {Filomat},
     pages = {1065 },
     year = {2021},
     volume = {35},
     number = {4},
     doi = {10.2298/FIL2104065C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2104065C/}
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