References
- [1] ADEGOKE, K.: A master identity for Horadam numbers, preprint, 2019; available at https://arxiv.org/abs/1903.11057.
- [2] ADEGOKE, K.: Weighted tribonacci sums, Konuralp J. Math. 8 (2020), no. 2, 355–360.
- [3] ADEGOKE, K.—FRONTCZAK, R.—GOY, T.: Partial sum of the products of the Horadam numbers with indices in arithmetic progression, Notes Number Theory Discrete Math. 27 (2021), no. 2, 54–63.
- [4] FRONTCZAK, R.: A short remark on Horadam identities with binomial coefficients, Ann. Math. Inform. 54 (2021), 5–13.
- [5] GOY, T.: Horadam sequence through recurrent determinants of tridiagonal matrix, Kragujevac J. Math. 42 (2018), no. 4, 527–532.
- [6] GOY, T.—SHATTUCK, M.: Determinants of Toeplitz-Hessenberg matrices with generalized Fibonacci entries, Notes Number Theory Discrete Math. 25 (2019), no. 4, 83–95.
- [7] HORADAM, A. F.: A generalized Fibonacci sequence, Amer. Math. Monthly 68 (1961), no. 5, 455–459.
- [8] HORADAM, A. F.: Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (1965), no. 3, 161–176.
- [9] HORADAM, A. F.: Pell identities, Fibonacci Quart. 9 (1971), no. 3, 245–252, 263.
- [10] KILIÇ, E.—ARIKAN, T.: Double binomial sums and double sums related with certain linear recurrences of various order, Chiang Mai J. Sci. 45 (2018), no. 3, 1569–1577.
- [11] KOSHY, T.: Fibonacci and Lucas Numbers with Applications, Vol. 1. Second edition of [MR1855020]. In: Pure and Applied Mathematics (Hoboken). John Wiley & Sons, Inc., Hoboken, NJ, 2018.
- [12] KOSHY, T.: Fibonacci and Lucas Numbers with Applications, Vol. 2, In: Pure and Applied Mathematics (Hoboken). John Wiley & Sons, Inc., Hoboken, NJ, 2019.
- [13] LARCOMBE, P. J.: Horadam sequences: a survey update and extension, Bull. Inst. Combin. Appl. 80 (2017), 99–118.
- [14] LARCOMBE, P. J.—BAGDASAR, O. D.—FENNESSEY, E. J.: Horadam sequences: a survey, Bull. Inst. Combin. Appl. 67 (2013), 49–72.
- [15] ÖMÜR, N.—DURAN, Ö.: On binomial triple sums involving Fibonacci and Lucas numbers, Honam Math. J. 42 (2020), no. 1, 49–62.
- [16] RIBENBOIM, P.: My Numbers, my Friends. (Popular lectures on number theory). Springer-Verlag, New York, 2000.
- [17] STĂNICĂ, P.: Generating functions, weighted and non-weighted sums for powers of second order recurrence sequences, Fibonacci Quart. 41 (2003), no. 4, 321–333.
- [18] TAŞDEMIR, F.: Binomial triple sums with the Lucas numbers, Punjab Univ. J. Math. 52 (2020), no. 7, 37–43.
- [19] TAŞDEMIR, F.: Triple sums including Fibonacci numbers with three binomial coefficients, Notes on Number Theory and Discrete Math. 27 (2021), no. 1, 188–197.
- [20] TAŞDEMIR, F.—TOSKA, T. G.: Formulas for binomial double sums related to Lucas numbers, Ars Combin. 152 (2020), 235–246.
- [21] VAJDA, S.: Fibonacci & Lucas Numbers, and the Golden Section: Theory and Applications. Courier Corporation, Dover Press, 2008.