Titlebook: Applications of Fibonacci Numbers; Volume 9: Proceeding Frederic T. Howard Conference proceedings 2004 Springer Science+Business Media Dord

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Chih-Chang Chang,Lung-Ming Fu,Ruey-Jen YangThe Bernoulli numbers .. may be defined by means of the generating function .. An example of a “lacuary” recurrence for these numbers is .. This recurrence has lacunae, or gaps, or length 6. That is, to compute .., it is not necessary to know the values of .. for all . < 6.; we need only know the values of .. for . = 0, 1, ..., . - 1.

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AC Dielectrophoresis Lab-on-Chip DevicesConsider the Fibonacci sequence (..)..

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Universal Bernoulli Polynomials and P-Adic Congruences,The .. are defined by

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Recounting Binomial Fibonacci Identities,In [4], Carlitz demonstrates . using sophisticated matrix methods and Binet’s formula. Nevertheless, the presence of binomial coefficients suggests that an elementary combinatorial proof should be possible. In this paper, we present such a proof, leading to other Fibonacci identities.

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