The Fibonacci sequence can be obtained by drawing diagonals in a Pascal’s triangle, and from this, we can obtain the Lucas identity. An investigation on the behavior of certain kinds of other diagonals inside a Pascal’s triangle identifies a new family of recursive sequences: the k-Padovan sequences. This family both contains the Fibonacci and the Padovan sequences. A general binomial identity for k-Padovan sequences which extends both the well-known Lucas identity and the less known Padovan identity is derived.
An extension of Lucas identity via Pascal’s triangle
Vincenzi, Giovanni
2021-01-01
Abstract
The Fibonacci sequence can be obtained by drawing diagonals in a Pascal’s triangle, and from this, we can obtain the Lucas identity. An investigation on the behavior of certain kinds of other diagonals inside a Pascal’s triangle identifies a new family of recursive sequences: the k-Padovan sequences. This family both contains the Fibonacci and the Padovan sequences. A general binomial identity for k-Padovan sequences which extends both the well-known Lucas identity and the less known Padovan identity is derived.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
