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Adegoke, Kunle; Frontczak, Robert; Goy, Taras

Binomial tribonacci sums. (English) Zbl 1513.11032

DML, Discrete Math. Lett. 8, 30-37 (2022).
Summary: We derive expressions for several binomials sums involving a generalized tribonacci sequence. We also study double binomial sums involving this sequence. Several explicit examples involving tribonacci and tribonacci-Lucas numbers are stated to highlight the results.

Cited in 1 Document

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations

Keywords:

generalized tribonacci sequence; tribonacci number; tribonacci-Lucas number; binomial transform

Software:

OEIS
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Full Text: DOI
OA License

Online Encyclopedia of Integer Sequences:

a(n) = a(n-1) + a(n-2) + a(n-3), a(0)=3, a(1)=1, a(2)=3.

References:

[1] K. Adegoke, Weighted tribonacci sums, Konuralp J. Math. 8 (2020) 355-360.
[2] K. Adegoke, R. Frontczak, T. Goy, Special sums with squared Horadam numbers and generalized Tribonacci numbers, Palest. J. Math. (2021), To appear. · Zbl 1471.11031
[3] K. Adegoke, A. Olatinwo, W. Oyekanmi, New Tribonacci recurrence relations and addition formulas, Notes Number Theory Discrete Math. 26 (2020) 164-172.
[4] P. Anantakitpaisal, K. Kuhapatanakul, Reciprocal sums of the tribonacci numbers, J. Integer Seq. 19 (2016) #16.2.1. · Zbl 1364.11037
[5] K. N. Boyadzhiev, Notes on the Binomial Transform: Theory and Table with Appendix on Stirling Transform, World Scientific, Singapore, 2018. · Zbl 1432.11001
[6] M. Catalani, Identities for Tribonacci-related sequences, arXiv:0209179 [math.CO], (2002).
[7] G. Cerda-Morales, Quadratic approximation of generalized tribonacci sequences, Discuss. Math. Gen. Algebra Appl. 38 (2018) 227-237. · Zbl 1463.11035
[8] E. Choi, Modular tribonacci numbers by matrix method, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 20 (2013) 207-221. · Zbl 1358.11027
[9] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel, Dordrecht, 1974. · Zbl 0283.05001
[10] J. Feng, More identities on the Tribonacci numbers, Ars Combin. 100 (2011) 73-78. · Zbl 1265.11023
[11] R. Frontczak, A short remark on Horadam identities with binomial coefficients, Ann. Math. Inf. 54 (2021) DOI: 10.33039/ami.2021.03.016, In press. · Zbl 1499.11063 · doi:10.33039/ami.2021.03.016
[12] R. Frontczak, Convolutions for generalized Tribonacci numbers and related results, Int. J. Math. Anal. 12 (2018) 307-324.
[13] R. Frontczak, Relations for generalized Fibonacci and Tribonacci sequences, Notes Number Theory Discrete Math. 25 (2019) 178-192.
[14] R. Frontczak, Sums of Tribonacci and Tribonacci-Lucas numbers, Int. J. Math. Anal. 12 (2018) 19-24.
[15] T. Goy, M. Shattuck, Determinant identities for Toeplitz-Hessenberg martices with tribonacci number entries, Trans. Comb. 9 (2020) 89-109. · Zbl 1463.05017
[16] M. Janjić, Words and linear recurrences, J. Integer Seq. 21 (2018) #18.1.4. · Zbl 1384.05011
[17] T. Komatsu, R. Li, Convolution identities for Tribonacci numbers with symmetric formulae, Math. Rep. 21(71) (2019) 27-47. · Zbl 1463.11041
[18] K. Kuhapatanakul, L. Sukruan, The generalized tribonacci numbers with negative subscripts, Integers 14 (2014) #A32. · Zbl 1295.11014
[19] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, https://oeis.org. · Zbl 1044.11108
[20] Y. Soykan, Tribonacci and Tribonacci-Lucas matrix sequences with negative subscripts, Comm. Math. Appl. 11 (2020) 141-159.
[21] N. Yilmaz, N. Taskara, Tribonacci and Tribonacci-Lucas numbers via the determinants of special matrices, Appl. Math. Sci. 8 (2014) 1947-1955.
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