Fibonacci sequences and group theory
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.
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متن کاملOn Fibonacci-Like Sequences
In this note, we study Fibonacci-like sequences that are defined by the recurrence Sk = a, Sk+1 = b, Sn+2 ≡ Sn+1 + Sn (mod n + 2) for all n ≥ k, where k, a, b ∈ N, 0 ≤ a < k, 0 ≤ b < k + 1, and (a, b) 6= (0, 0). We will show that the number α = 0.SkSk+1Sk+2 · · · is irrational. We also propose a conjecture on the pattern of the sequence {Sn}n≥k.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1973
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700043495