On the Mersenne sequence. (English) Zbl 1374.11020

Catarino, Paula; Campos, Helena; Vasco, Paulo

Ann. Math. Inform. 46, 37-53 (2016).

Summary: From Binet’s formula of Mersenne sequence we get some properties for this sequence. Mersenne, Jacobsthal and Jacobsthal-Lucas sequences are considered in order to achieve some relations between them, sums and certain products involving terms of these sequences. We also present some results with matrices involving Mersenne numbers such as the generating matrix, tridiagonal matrices and circulant type matrices.

MSC:

11B39	Fibonacci and Lucas numbers and polynomials and generalizations
15B36	Matrices of integers
11C20	Matrices, determinants in number theory

Keywords:

Mersenne numbers; Jacobsthal numbers; Jacobsthal-Lucas numbers; \(g\)-circulant matrix