Sequences with M-bonacci property and their finite sums
15 Aug 2008-International Journal of Mathematical Education in Science and Technology (Taylor & Francis Group)-Vol. 39, Iss: 6, pp 819-829
TL;DR: In this article, two summation formulas for sequences with M-bonacci property were derived and applied to the arithmetic series, mth g − gonal numbers and the Fibonacci series.
Abstract: The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, mth g − gonal numbers and the Fibonacci series are demonstrated.
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TL;DR: In this paper, the authors constructed infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigated the convergence of the series to an integer.
Abstract: n this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.
4 citations
TL;DR: In this article, the M-bonacci binomial coefficients were introduced, which are similar to the binomial and the Fibonomial coefficients and can be displayed in a triangle similar to Pascal's triangle from which some identities become obvious.
Abstract: In this note, we introduce M-bonomial coefficients or (M-bonacci binomial coefficients). These are similar to the binomial and the Fibonomial (or Fibonacci-binomial) coefficients and can be displayed in a triangle similar to Pascal's triangle from which some identities become obvious.
4 citations
TL;DR: In this paper, the ratio between consecutive terms of the sequence of row-sum was studied, and a generalization of the formula for binomial coefficients was given, where G is an mth g-gonal number.
Abstract: Formulae for row-sum of M-bonomial coefficients where G is an mth g-gonal number is developed from a study of the ratio between consecutive terms of the sequence of row-sum. The result generalizes the formula for row-sum of binomial coefficients: .
2 citations
Cites methods from "Sequences with M-bonacci property a..."
...A useful introduction to M-bonacci sequences can be found in [4,5]....
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14 Feb 2019
TL;DR: The notion of m-bonacci-sum graphs denoted by \(G_{m,n}\) for positive integers m, n are introduced and it is shown that this graph is bipartite and for \(n\ge 2^{m-2}\), \(\{1,2,\ldots ,n\) has exactly \((m-1)\) components.
Abstract: We introduce the notion of m-bonacci-sum graphs denoted by \(G_{m,n}\) for positive integers m, n. The vertices of \(G_{m,n}\) are \(1,2,\ldots ,n\) and any two vertices are adjacent if and only if their sum is an m-bonacci number. We show that \(G_{m,n}\) is bipartite and for \(n\ge 2^{m-2}\), \(G_{m,n}\) has exactly \((m-1)\) components. We also find the values of n such that \(G_{m,n}\) contains cycles as subgraphs. We also use this graph to partition the set \(\{1,2,\ldots ,n\}\) into \(m-1\) subsets such that each subset is ordered in such a way that sum of any 2 consecutive terms is an m-bonacci number.
1 citations
TL;DR: In this paper , the authors introduced the notion of m-bonacci-sum graphs for positive integers m,n, where the vertices of Gm,n are 1,2,…,n and any two vertices are adjacent if and only if their sum is an m-Bonacci number.
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TL;DR: In this paper, two new summation formulas for M-bonacci numbers are given, which are generalizations of the two summation formula for Fibonacci numbers, and the formulas are shown to be equivalent to the two formulas for the M-Bonacci numbers.
Abstract: The note considers M-bonacci numbers, which are a generalization of Fibonacci numbers. Two new summation formulas for M-bonacci numbers are given. The formulas are generalizations of the two summation formulas for Fibonacci numbers.
9 citations
TL;DR: In this article, various approaches to determining the sum of finite and infinite series with Fibonacci numbers are considered. But the main focus of this paper is on finite series and not infinite series.
Abstract: In this article, certain finite and infinite series which involve the Fibonacci numbers in some way are discussed. Various approaches to determining the sum of these series are considered. The material should serve to stimulate readers and their students to seek other proofs of these sums, and ones for similar series, as well as demonstrating the different approaches to tackling problems of this type. An interesting aspect of the sums of infinite series is highlighted and suggestions for generalization of both types of series are also given.
6 citations