Affiliation:
1. Obafemi Awolowo University , Ile-Ife , Nigeria
2. Landesbank Baden-Württemberg , Stuttgart , Germany
3. Vasyl Stefanyk Precarpathian National University , Ivano-Frankivsk , Ukraine
Abstract
Abstract
We derive recurrence relations for the squares of the Horadam numbers
w
n
2
w_n^2
, where the Horadam sequence w
n
is such that the numbers w
n
, for n ∈ ℤ, are defined recursively by w
0 = a, w
1 = b, w
n
= pw
n−
1
− qw
n−
2 (n ≥ 2), where a, b, p and q are arbitrary complex numbers with p ≠ 0 and q ≠ 0. Some related results emanating from the recurrence relations such as reciprocal sums, partial sums, and sums with double binomial coefficients are also presented.
Reference21 articles.
1. [1] ADEGOKE, K.: A master identity for Horadam numbers, preprint, 2019; available at https://arxiv.org/abs/1903.11057.
2. [2] ADEGOKE, K.: Weighted tribonacci sums, Konuralp J. Math. 8 (2020), no. 2, 355–360.
3. [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. [4] FRONTCZAK, R.: A short remark on Horadam identities with binomial coefficients, Ann. Math. Inform. 54 (2021), 5–13.
5. [5] GOY, T.: Horadam sequence through recurrent determinants of tridiagonal matrix, Kragujevac J. Math. 42 (2018), no. 4, 527–532.