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Some algebraic relations on integer sequences involving oblong and balancing numbers

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Tekcan, Ahmet
Eraşık, Meltem E.

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Özkoç, Arzu

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Charles Babbage Research Centre

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Abstract

Let k >= 0 be an integer. Oblong (pronic) numbers are numbers of the form O-k = k(k+1). In this work, we set a new integer sequence B = B-n(k) defined as B-0 = 0, B-1 = 1 and B-n = O-k Bn-1 - Bn-2 for n >= 2 and then derived some algebraic relations on it. Later, we give some new results on balancing numbers via oblong numbers.

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Mathematics, Fibonacci numbers, Lucas numbers, Pell numbers, Oblong numbers, Balancing numbers, Binary linear recurrences, Circulant matrix, Spectral norm, Simple continued fraction expansion, Cross-ratio

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Tekcan, A. vd. (2016). "Some algebraic relations on integer sequences involving oblong and balancing numbers". Ars Combinatoria, 128, 11-31.

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