On Sum Formulas for Generalized Tribonacci Sequence

Main Article Content

Yüksel Soykan


In this paper, closed forms of the sum formulas for generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third-order linear recurrance sequences.

Tribonacci numbers, Padovan numbers, Perrin numbers, sum formulas

Article Details

How to Cite
Soykan, Y. (2020). On Sum Formulas for Generalized Tribonacci Sequence. Journal of Scientific Research and Reports, 26(7), 27-52. https://doi.org/10.9734/jsrr/2020/v26i730283
Original Research Article


Bruce I. A modified Tribonacci sequence. Fibonacci Quarterly. 1984;22(3):244-246. Soykan; JSRR, 26(7): 27-52, 2020; Article no.JSRR.60366 Catalani M. Identities for Tribonacci-related sequences; 2002. arXiv:math/0209179
Choi E. Modular Tribonacci numbers by matrix method. Journal of the Korean Society of Mathematical Education
Series B: Pure and Applied. Mathematics.

Elia M. Derived sequences, The Tribonacci recurrence and cubic forms. Fibonacci Quarterly. 2001;39(2):107-115.

Lin PY. De moivre-type identities for the Tribonacci numbers. Fibonacci Quarterly.

Pethe S. Some Identities for Tribonacci sequences. Fibonacci Quarterly.

Scott A, Delaney T, Hoggatt Jr., V. The Tribonacci sequence. Fibonacci Quarterly.

Shannon AG, Horadam AF. Some properties of third-order recurrence relations. The Fibonacci Quarterly.

Shannon A. Tribonacci numbers and Pascal’s pyramid. Fibonacci Quarterly.

Spickerman W. Binet’s formula for the Tribonacci sequence. Fibonacci Quarterly.

Yalavigi CC. A note on ‘another generalized Fibonacci sequence. The Mathematics Student. 1971;39:407-408.

Yalavigi CC. Properties of Tribonacci numbers. Fibonacci Quarterly.

Yilmaz N, Taskara N. Tribonacci and Tribonacci-Lucas numbers via the determinants of special matrices. Applied
Mathematical Sciences. 2014;8(39):1947- Marcellus E. Waddill. Using matrix techniques to establish properties of
a generalized Tribonacci sequence. In Applications of Fibonacci Numbers, Volume , G. E. Bergum et al., Eds.). Kluwer Academic Publishers. Dordrecht, The Netherlands. 1991;299-308.

Sloane NJA. The on-line encyclopedia of integer sequences.

Soykan Y. On four special cases of generalized Tribonacci sequence: Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas and adjusted Tribonacci-Lucas Sequences.

Soykan Y. On generalized third-order pell numbers.

Soykan Y. On generalized Padovan numbers. MathLAB Journal, In Print. Soykan Y. Generalized Pell-Padovan numbers.

Soykan Y. A study on generalized Jacobsthal-Padovan numbers. Earthline Journal of Mathematical Sciences.

Soykan Y. On generalized Narayana numbers. Int. J. Adv. Appl. Math. and Mech.
(ISSN: 2347-2529)

PolatlıEE, Soykan Y. On generalized thirdorder Jacobsthal numbers. Submitted. Soykan Y. On generalized Grahaml numbers.

Soykan Y. On generalized reverse 3-primes numbers. Journal of Scientific Research and Reports. 2020;26(6):1-20.

G¨okbas¸ H, K¨ose H. Some sum formulas for products of pell and pell-lucas numbers. Int. J. Adv. Appl. Math. and Mech. 2017;4(4):1-

Koshy T. Fibonacci and Lucas numbers with applications. A Wiley-Interscience Publication, New York; 2001.

Koshy T. Pell and Pell-Lucas numbers with applications. Springer, New York; 2014.

Hansen RT. General identities for linear Fibonacci and Lucas summations.

Fibonacci Quarterly. 1978;16(2):121- Soykan Y. On summing formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers.

Soykan; JSRR, 26(7): 27-52, 2020; Article no.JSRR.60366 Soykan Y. Corrigendum: On summing formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers;

Corrigendum On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers Soykan Y. On summing formulas for Horadam numbers.
DOI: 10.9734/AJARR/2020/v8i130192

Soykan Y. Generalized Fibonacci numbers: Sum formulas. Journal of Advances in Mathematics and Computer Science.

Frontczak R. Sums of Tribonacci and Tribonacci-Lucas numbers. International

Parpar T. k’ncı Mertebeden Rek¨ urans Bag˘ ıntısının O¨ zellikleri ve Bazı Uygulamaları, Selc¸uk U¨ niversitesi, Fen Bilimleri Enstit ¨us¨ u, Y¨uksek Lisans Tezi; Soykan Y. Summing formulas for generalized Tribonacci numbers. Universal Journal of Mathematics and Applications. ;3(1):1-11.ISSN 2619-9653
DOI: https://doi.org/10.32323/ujma.637876

Soykan Y. Matrix sequences of Tribonacci and Tribonacci-Lucas numbers; 2018. arXiv:1809.07809v1 [math.NT]

Soykan. Summation formulas for generalized Tetranacci numbers.

Waddill ME. The Tetranacci sequence and generalizations. Fibonacci Quarterly.

Soykan Y. Linear summing formulas of generalized Pentanacci and Gaussian generalized Pentanacci numbers. Science. 2019;33(3):1-14.

Soykan Y. Sum formulas for generalized fifth-order linear recurrence sequences.

Article no.JAMCS.53303, ISSN: 2456-9968

Soykan Y. On summing formulas of generalized Hexanacci and Gaussian generalized Hexanacci numbers.
Article no.ARJOM.50727