Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On the generalized Fibonacci sequence. (English)
Authors: Kolesnik Alexander
The explicit combinatorial formula for calculation the general member of the sequence is obtained.
Abstract
The generalized Fibonacci sequence $c_0 = {\beta}$, \ $c_1 = {\alpha}$, $c_n = ac_{n-1} + bc_{n-2}$, $n{\ge 2},$ is considered, where ${\alpha}, {\beta}, a, b$ are the elements of an arbitrary commutative ring with unit.The explicit combinatorial formula for calculation the general member of the sequence is obtained.
Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova
str. Academiei 5, MD-2028 Chişinău, Moldova
Contents
- Morita contexts and correspondences between lattices of submodules. (Russian)
- A theorem on union of $d$-star-shaped sets. (Russian)
- Planar point groups of tablets and hypertablets $P$-symmetries and their application to the study of multidimensional symmetry groups. (Russian)
- On the generalized Fibonacci sequence. (English)
- Idempotents and the radical with respect to a right ideal. II. (Russian)
- Concordant solutions of linear multidimensional differential equations. (Russian)
- On the completeness of topological modules free in some classes. (English)
- The principle of composition of multidimensional dynamical systems. (Russian)
- Algorithms of choice of optimal configurations in weighted digraphs. (Russian)
- The construction of a numerable collection of precomplete classes of formulae in the provability logic. (English)
- On the strong isomorphism of groups and isomorphism of $P$-symmetries. (Russian)
- Uniqueness of topologies in the case of some constructions of rings and modules. (Russian)
