On the Combinatorial Properties of Bihyperbolic Balancing Numbers

[1] BILGIN, M.—ERSOY, S.: Algebraic Properties of Bihyperbolic Numbers, Adv. Appl. Clifford Algebr. 30 (2020), no. 1, 1–13.10.1007/s00006-019-1036-2Search in Google Scholar

[2] BEHERA, A.—PANDA, G. K.: On the square roots of triangular numbers, Fibonacci Quart. 37 (1999), no. 2, 98–105.Search in Google Scholar

[3] CATARINO, P.—CAMPOS, H.—VASCO, P.: On some identities for balancing and cobalancing numbers, Ann. Math. Inform. 45 (2015), 11–24.Search in Google Scholar

[4] COCKLE, J.: On certain functions resembling quaternions, and on a new imaginary in algebra, Lond. Edinb. Dubl. Phil. Mag. 33 (1848), 435–439.10.1080/14786444808646139Search in Google Scholar

[5] COCKLE, J.: On a new imaginary in algebra, Lond. Edinb. Dubl. Phil. Mag. 34 (1849), 37–47.10.1080/14786444908646169Search in Google Scholar

[6] COCKLE, J.: On the symbols of algebra, and on the theory of tesarines, Lond. Edinb. Dubl. Phil. Mag. 34 (1849), 406–410.10.1080/14786444908646257Search in Google Scholar

[7] COCKLE, J.: On impossible equations, on impossible quantities, and on tesarines, Lond. Edinb. Dubl. Phil. Mag. 37 (1850), 281–283.10.1080/14786445008646598Search in Google Scholar

[8] PANDA, G. K.: Some fascinating properties of balancing numbers,In: Proc.Eleventh Internat. Conference on Fibonacci Numbers and Their Applications, Congr. Numer. Vol. 194 (2009), pp. 185–189.Search in Google Scholar

[9] PANDA, G. K.: Sequence balancing and cobalancing numbers, Fibonacci Quart. 45 (2007), no. 3, 265–271.Search in Google Scholar

[10] PANDA, G. K.—RAY, P. K.: Cobalancing numbers and cobalancers,Int. J. Math. Math. Sci. 8 (2005), 1189–1200.10.1155/IJMMS.2005.1189Search in Google Scholar

[11] POGORUI, A. A.—RODŔIGUEZ-DAGNINO, R. M.—RODŔIGUEZ-SAID, R. D.: On the set of zeros of bihyperbolic polynomials, Complex Var. Elliptic Equ. 53 (2008), no. 7, 685–690.10.1080/17476930801973014Search in Google Scholar

[12] ROCHON, D.—SHAPIRO, M.: On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea, Fasc. Mat. 11 (2004), 71–110.Search in Google Scholar

[13] RAY, P. K.: Certain Matrices Associated with Balancing and Lucas-balancing Numbers, Matematika 28 (2012), no. 1, 15–22.Search in Google Scholar

[14] RAY, P. K.— SAHU, J.: Generating functions for certain balancing and Lucas-balancing numbers,Palest. J. Math. 5 (2016), no. 2, 122–129.10.12697/ACUTM.2016.20.14Search in Google Scholar