Iterated Binomial Transforms of the k-Fibonacci Sequence
نویسندگان
چکیده
منابع مشابه
Toeplitz transforms of Fibonacci sequences
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
متن کاملtoeplitz transforms of fibonacci sequences
we introduce a matricial toeplitz transform and prove that the toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. we investigate the injectivity of this transform and show how this distinguishes the fibonacci sequence among other recurrence sequences. we then obtain new fibonacci identities as an application of our transform.
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To facilitate rapid numerical calculations of identities pertaining to Fibonacci numbers, we present each identity as a binomial sum. Mathematics Subject Classification: 05A10,11B39
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Numerous writers appear to have been fascinated by the many interesting summation identitites involving the Fibonacci and related Lucas numbers. Various types of formulas are discussed and various methods are used. Some involve binomial coefficients [2 ] , [4 ] . Generating function methods are used in [2] and [5] and higher powers appear in [6] . Combinations of these or other approaches appea...
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ژورنال
عنوان ژورنال: British Journal of Mathematics & Computer Science
سال: 2014
ISSN: 2231-0851
DOI: 10.9734/bjmcs/2014/11783