Weighted Tribonacci Sums

Year 2020, Volume: 8 Issue: 2 , 355 - 360 , 27.10.2020

Kunle Adegoke

https://izlik.org/JA68MB45NX

Abstract

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

Keywords

Tribonacci numbers , weighted sums , binomial sums

References

• [1] K. Adegoke, Weighted sums of some second-order sequences, arXiv:1803.09054[math.NT] (2018).
• [2] P. Anantakitpaisal and K. Kuhapatanakul, Reciprocal sums of the Tribonacci numbers, Journal of Integer sequences 19 (2016), 1–9.
• [3] J. Feng, More identities on the Tribonacci numbers, Ars Combinatorial C (2011), 73–78.
• [4] R. Frontczak, Sums of Tribonacci and Tribonacci-Lucas numbers, International Journal of Mathematical Analysis 12:1 (2018), 19–24.
• [5] N. Irmak and M. Alp, Tribonacci numbers with indices in arithmetic progression and their sums, Miskolc Mathematical Notes 14:1 (2013), 125–133.
• [6] E. Kilic, Tribonacci sequences with certain indices and their sums, Ars Combinatorial 86 (2008), 13–22.
• [7] D. V. Shah, Some Tribonacci identities, Mathematics Today 27 (2011), 1–9.