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A Generalized Fibonacci Sequence
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A Synthesis of Certain Polynomial Sequences
Encouraged by the comments of the reviewer [1] of my earlier article [4], I now take the opportunity to extend the material in [4] to incorporate some new thoughts on general recursively-definedExpand
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A PARTIAL ASYMPTOTIC FORMULA FOR THE NIVEN NUMBERS
A Niven number is a positive integer that is divisible by its digital sum. That is, if n is an integer and s(n) denotes the digital sum of n, then n is a Niven number if and only if sin) is a factorExpand
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Derivative Sequences of Fibonacci and Lucas Polynomials
Let us consider the Fibonacci polynomials U n(x) and the Lucas polynomials V n (x) (or simply U n and Vn, if there is no danger of confusion) defined as $$ {U_n} = x{U_{n - 1}} + {U_{n - 2}}({U_0}Expand
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Some Relationships among Vieta, Morgan-Voyce and Jacobsthal Polynomials
We define below the Morgan-Voyce polynomials B n(x) and b n(x) [21], and the ‘companion’ Morgan-Voyce polynomials C n(x) and c n(x) which were found in embryonic form in [26] and formalized,Expand
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Fibonacci Number Triples
where I=2(p-qb), m=2(p-gqa), a= l (1 + \15), b-(1-\/5). The purpose of this article is to find a connection between generalized Fibonacci numbers and Pythagorean number triples. By a PythagoreanExpand
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Divisibility properties of some fibonacci-type sequences
A generalized Fibonacci-type sequence is defined from a fourth order homogeneous linear recurrence relation, and various divisibility properties are developed. In particular, the notion of a properExpand
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