نتایج جستجو برای: fibonacci sequence
تعداد نتایج: 408412 فیلتر نتایج به سال:
Herein we investigate the historical origins of the Fibonacci numbers. After emphasising the importance of these numbers, we examine a standard conjecture concerning their origin only to demonstrate that it is not supported by historical chronology. Based on more recent findings, we propose instead an alternative conjecture through a close examination of the historical and historical/mathematic...
Taking the Fibonacci sequence G0 = 1; G1 = b 2 f1; 3; 5g and Gn+1 = 3 Gn + Gn 1 (n 1) with an integer 2 m 2 N , we get a purely periodic sequence fGn( mod m)g. Consider any shortest full period and form a frequency block Bm 2 N to consist of the frequency values of the residue d when d runs through the complete residue system modulo m. The purpose of this paper is to show that such frequency bl...
A Smarandache-Fibonacci triple is a sequence S(n), n ≥ 0 such that S(n) = S(n − 1) + S(n − 2), where S(n) is the Smarandache function for integers n ≥ 0. Clearly, it is a generalization of Fibonacci sequence and Lucas sequence. Let G be a (p, q)-graph and {S(n)|n ≥ 0} a Smarandache-Fibonacci triple. An bijection f : V (G) → {S(0), S(1), S(2), . . . , S(q)} is said to be a super Smarandache-Fibo...
Summation rules for various types of convolutions have been the subject of much interest in The Fibonacci Quarterly. The following references are of particular relevance to this topic: Cohen and Hudson [8], Corley [9], Filipponi and Freitag [11], Gould [14], Haukkanen [15], Hsu [19], and finally Philippou and Georghiou [23]. Also consult Neuman and Schonbach’s SIAM Review article [22], where su...
The Fibonacci and Lucas sequences have been generalized in many ways, some by preserving the initial conditions, others recurrence relation. One of them is defined relation B_n = B_{n−1} + B_{n−2}, n >= 2 with condition B_0 2s, B_1 s 1 where Z. In this paper, we consider reciprocal sums B^2_n, an established result that also involve Bn.
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