TY - JOUR
AU - Frontczak, R.
AU - Goy, T.P.
PY - 2020/06/12
Y2 - 2020/09/29
TI - Mersenne-Horadam identities using generating functions
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 12
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.12.1.34-45
UR - https://scijournals.pnu.edu.ua/index.php/cmp/article/view/3870
SP - 34-45
AB - The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and $w_1=b$, where $a$, $b$, $p>0$ and $q
e0$ are integers. This is achieved by relating the respective (ordinary and exponential) generating functions to each other. Several explicit examples involving Fibonacci, Lucas, Pell, Jacobsthal and balancing numbers are stated to highlight the results.
ER -