Does the Padovan Spiral or the plastic number occur in nature like the Fibonacci Spiral and golden ratio do? Could it be that some of the things we associate with the Fibonanci spiral are better fit with the …

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences.

If an increasing sequence of non-negative integers has the property that the largest of any four consecutive terms equals the sum of the two smallest, then the sequence is a linear combination of …

Corollary 2.5. The only common values of Padovan and Perrin sequences are 0, ±1, ±2, ±3, 4, 5, ±7, 10, 12, 25, 86.

Abstract Let (Pn)n>0 be the Padovan sequence given by P0 = 1, P1 = P2 = 0 and the recurrence formula Pn+3 = Pn+1 + Pn, for all n > 0. In this note we study and completely solve the Diophantine …

ON THE PADOVAN SEQUENCE ALAIN FAISANT Abstract. The aim of this article is to give some properties of the so-called Padovan sequence (Tn)n≥0 defined by Tn+3 = Tn+1 + Tn for all n ∈ N, T1 …

The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom Hans van der Laan: Modern Primitive.