Fibonacci and Lucas numbers, by Verner E. Hoggatt Jr. Houghton Mifflin Company, Boston, 1969. 92 pages. [PDF]
, 1969 Herbert London
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Edge-Disjoint Fibonacci Trees in Hypercube
Journal of Computer Networks and Communications, 2014 The Fibonacci tree is a rooted binary tree whose number of vertices admit a recursive definition similar to the Fibonacci numbers. In this paper, we prove that a hypercube of dimension h admits two edge-disjoint Fibonacci trees of height h, two edge ...
Indhumathi Raman, Lakshmanan Kuppusamy
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On the sum of reciprocal generalized Fibonacci numbers [PDF]
arXiv, 2015 In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
arxiv
Popular Lectures in Mathematics—(i) The Method of Mathematical Induction by I. S. Sominskii, (ii) Fibonacci Numbers by N. N. Vorob'ev, (iii) Some Applications of Mechanics to Mathematics by v. A. Uspenskh, (iv) Geometrical Constructions Using Compasses Only by A. N. Kostovskii, (V) The Ruler in Geometrical Constructions by A. S. Smogorzhevskii, (vi) Inequalities by P. P. Korovkin (Pergamon Press, Oxford, 1961). [PDF]
, 1962 R. P. Gillespie
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Four New Generalized Fibonacci Number Summation Identities [PDF]
arXiv, 2018 Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of which two special cases are already known in literature.
arxiv
Fibonacci Numbers in Coin Tossing Sequences [PDF]
, 1978 Mark Finkelstein, Robert Whitley
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Three closed forms for convolved Fibonacci numbers
Results in Nonlinear Analysis, 2020 In the paper, by virtue of the Faà di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three
Feng Qi
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Identities and Generating Functions of Products of Generalized Fibonacci numbers, Catalan and Harmonic Numbers [PDF]
arXivWe considered the properties of generalized Fibonacci and Lucas numbers class. The analogues of well-known Fibonacci identities for generalized numbers are obtained. We gained a new identity of product convolution of generalized Fibonacci and Lucas numbers.
arxiv
Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers [PDF]
arXiv, 2007 The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order. And the question is: are Pauli rabbits killer rabbits?
arxiv