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Binet type formula for Tribonacci sequence with arbitrary initial numbers

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  • Ilija, Tanackov

Abstract

This paper presents detailed procedure for determining the formula for calculation Tribonacci sequence numbers with arbitrary initial numbers Ta,b,c,(n). Initial solution is based on the concept of damped oscillations of Lucas type series with initial numbers T3,1,3(n). Afterwards coefficient θ3 has been determined which reduces Lucas type Tribonacci series to Tribonacci sequence T0,0,1(n). Determined relation had to be corrected with a phase shift ω3. With known relations of unitary series T0,0,1(n) with remaining two equations of Tribonacci series sequence T1,0,0(n) and T0,1,0(n), Binet type equation of Tribonacci sequence that has initial numbers Ta,b,c(n) is obtained.

Suggested Citation

  • Ilija, Tanackov, 2018. "Binet type formula for Tribonacci sequence with arbitrary initial numbers," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 63-68.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:63-68
    DOI: 10.1016/j.chaos.2018.06.023
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    References listed on IDEAS

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    1. Tanackov, Ilija & Kovačević, Ilija & Tepić, Jovan, 2015. "Formula for Fibonacci sequence with arbitrary initial numbers," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 115-119.
    2. Rybołowicz, Bernard & Tereszkiewicz, Agnieszka, 2018. "Generalized tricobsthal and generalized tribonacci polynomials," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 297-308.
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