On identities with multinomial coefficients for Fibonacci-Narayana sequence

Abstract

In this paper we study some families of Toeplitz-Hessenberg determinants the entries of which are Fibonacci-Narayana (or Narayana's cows) numbers. This leads to discover some identities for these numbers. In particular, we establish connection between Fibonacci-Narayana numbers with Fibonacci and tribonacci numbers. We also present new formulas for Fibonacci-Narayana numbers via recurrent determinants of four-diagonal matrix.

Generalised (k, t)-Narayana sequence

“…Goy [10] studied Toeplitz-Hessenberg determinants with entries for Fibonacci-Narayana numbers or Narayana numbers. He established connections between determinants of Toeplitz-Hessenberg matrices with entries of Fibonacci-Narayana numbers and Fibonacci, Tribonacci numbers.…”

New Narayana Triangle

“…(2) where (3) The Narayana numbers and their properties have been studied by Özkan, Ramirez, Petersen, et al [3][4][5][6][7][8][9][10]. In particular, Petersen [5] places them in the Euler-Macmahon-Carlitz/Riordan combinatorial spectrum.…”

Permanent of Toeplitz Matrices With Narayana Entries by Ozen Ozer, Selcuk Koyuncu, and Wynn Kwiatkowski

“…There are a lot of relationships between determinantal and permanental representations of matrices and these sequences of integer(see,( [6], [5], [3], [4], [1])). Toeplitz-Hessenberg determinants with entries that are Fibonacci-Narayana (or Narayana's cows) numbers have been studied(see, [2]). In this paper, we study the permanent of Toeplitz matrices with Narayana entries.…”