Geodesic
On a two-parameter generalization of Jacobsthal numbers and its graph interpretation
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 72 (2018) no. 2.

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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.
Keywords: Jacobsthal numbers, generalized Jacobsthal numbers, Binet’s formula, generating function, graph interpretation, Merrifield-Simmons index 
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Bród, Dorota. On a two-parameter generalization of Jacobsthal numbers and its graph interpretation. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 72 (2018) no. 2. http://geodesic.mathdoc.fr/item/AUM_2018_72_2_a1/

[1] 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.

[2] Diestel, R., Graph Theory, Springer-Verlag, Heidelberg-New York, 2005.

[3] Falcon, S., On the k-Jacobsthal numbers, American Review of Mathematics and Statistics 2 (1) (2014), 67-77.

[4] 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.

[5] 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.

[6] Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quart. 34 (1) (1996), 40-54.

[7] Szynal-Liana, A., Włoch, A., Włoch, I., On generalized Pell numbers generated by Fibonacci and Lucas numbers, Ars Combin. 115 (2014), 411-423.

[8] Uygun, S., The (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequences, Applied Mathematical Sciences 9 (70) (2015), 3467-3476.