In this paper we introduce a two-parameter generalization of the classical Jacobsthal numbers ((s,p)-Jacobsthal numbers). We present some properties of the presented sequence, among others Binet’s formula, Cassini’s identity, the generating function. Moreover, we give a graph interpretation of (s,p)-Jacobsthal numbers, related to independence in graphs.
@article{bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_21,
author = {Dorota Br\'od},
title = {On a two-parameter generalization of Jacobsthal numbers and its graph interpretation},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {72},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_21}
}
Dorota Bród. On a two-parameter generalization of Jacobsthal numbers and its graph interpretation. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 72 (2018) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_2_21/
Dasdemir, A., The representation, generalized Binet formula and sums of the generalized Jacobsthal p-sequence, Hittite Journal of Science and Engineering 3 (2) (2016), 99-104.
Diestel, R., Graph Theory, Springer-Verlag, Heidelberg-New York, 2005.
Falcon, S., On the k-Jacobsthal numbers, American Review of Mathematics and Statistics 2 (1) (2014), 67-77.
Gutman, I., Wagner, S., Maxima and minima of the Hosoya index and the Merrifield-Simmons index: a survey of results and techniques, Acta Appl. Math. 112 (3) (2010), 323-348.
Jhala, D., Sisodiya, K., Rathore, G. P. S., On some identities for k-Jacobsthal numbers, Int. J. Math. Anal. (Ruse) 7 (9–12) (2013), 551-556.
Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quart. 34 (1) (1996), 40-54.
Szynal-Liana, A., Włoch, A., Włoch, I., On generalized Pell numbers generated by Fibonacci and Lucas numbers, Ars Combin. 115 (2014), 411-423.
Uygun, S., The (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequences, Applied Mathematical Sciences 9 (70) (2015), 3467-3476.