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Your search keyword '"Vincenzi, Giovanni"' showing total 3 results
3 results on '"Vincenzi, Giovanni"'

1. Padovan-like sequences and generalized Pascal's triangles.

Author

Anatriello, Giuseppina and Vincenzi, Giovanni

Subjects
*MATHEMATICAL models, *FIBONACCI sequence, *ARCHITECTS, *COMBINATORIAL identities, *PASCAL (Computer program language)
Abstract

The Padovan sequence and the Plastic number are mathematical objects of central interest among architects, and from this point of view, their importance is comparable to that of the Fibonacci sequence and the Golden mean. Padovan-like sequences, such as Perrin sequence or the Cordonnier sequence, also have mathematical applications. In this article, we will characterize a large family of Padovan-like sequences in terms of 'Padovan diagonals' of generalized Pascal's triangles. [ABSTRACT FROM AUTHOR]

Published
2020

2. Tribonacci-like sequences and generalized Pascal's pyramids.

Author

Anatriello, Giuseppina and Vincenzi, Giovanni

Subjects
*FIBONACCI sequence, *PASCAL'S triangle, *MATHEMATICS education, *NUMBER theory, *MATHEMATICS theorems, *EDUCATION
Abstract

A well-known result of Feinberg and Shannon states that the tribonacci sequence can be detected by the so-called Pascal's pyramid. Here we will show that any tribonacci-like sequence can be obtained by the diagonals of the Feinberg's triangle associated to a suitable generalized Pascal's pyramid. The results also extend similar properties of Fibonacci-like sequences. [ABSTRACT FROM AUTHOR]

Published
2014
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3. Generalized Pascal's triangles and associated [formula omitted]-Padovan-like sequences.

Author

Anatriello, Giuseppina, Németh, László, and Vincenzi, Giovanni

Subjects
*TRIANGLES, *LINEAR orderings, *FIBONACCI sequence
Abstract

One of the most interesting properties of Pascal's triangle is that the sequence of the sums of the elements on its diagonals is the best known recurrence sequence, the Fibonacci sequence. It is also known that other diagonals can be associated with other relevant recurrence sequences, such as the Padovan and k -Padovan sequences. In this paper, we see that similar properties also hold for diagonals of generalized Pascal's triangles. We show that the diagonal sums in generalized Pascal's triangles belong to the family of the so-called ' k -Padovan-like sequences' which are linear recurrences of order k with constant coefficients. A recurrence connection between the k -Padovan and k -Padovan-like sequences is derived. [ABSTRACT FROM AUTHOR]

Published
2022
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