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Osječki matematički list, Vol. 13 No. 1, 2013.

Professional paper

On the Padovan sequence

Bojan Kovačić orcid id orcid.org/0000-0002-3893-2191 ; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska
Luka Marohnić orcid id orcid.org/0000-0002-9431-7505 ; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska
Renata Opačić orcid id orcid.org/0000-0001-9800-7566 ; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska

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Abstract

The first few values of the Padovan sequence are defined geometrically in the introductory part of this paper. Next, by using a geometrical algorithm as a motivation, the Padovan sequence is defined by means of its recurrence relation and initial values. It is also shown how one could get an explicite formula for $P_{n}$ by using the plastic number. This is followed by the definition of morphic numbers and the proof that the plastic number
is a morphic number. Finally, some properties of the Padovan sequence are proven and some combinatorial interpretations are given.

Keywords

Padovan sequence; definition; basic properties; plastic number; morphic number; combinatorial interpretations

Hrčak ID:

105944

URI

https://hrcak.srce.hr/105944

Publication date:

30.8.2013.

Article data in other languages: croatian

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