Professional paper
On the Padovan sequence
Bojan Kovačić
orcid.org/0000-0002-3893-2191
; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska
Luka Marohnić
orcid.org/0000-0002-9431-7505
; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska
Renata Opačić
orcid.org/0000-0001-9800-7566
; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska
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
Publication date:
30.8.2013.
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