A new recursive formula arising from a determinantal expression for weighted Delannoy numbers

被引：8

作者：

DAGLI, Muhammet Cihat ^{[1
]}

机构：

[1] Akdeniz Univ, Fac Sci, Dept Math, Antalya, Turkey

来源：

TURKISH JOURNAL OF MATHEMATICS | 2021年 / 45卷 / 01期

关键词：

Delannoy number; central Delannoy number; determinantal expression; recurrence relation; FIBONACCI; POLYNOMIALS; TERMS;

D O I：

10.3906/mat-2009-92

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it. For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.

引用

页码：471 / 478

页数：8

共 34 条

[1] Why Delannoy numbers? [J].

Banderier, C ;

Schwer, S .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2005, 135 (01) :40-54

[2]

Bourbaki N., 2004, ELEMENTS MATH, DOI [10.1007/978-3-642-59315-4, DOI 10.1007/978-3-642-59315-4]

[3]

Cahill N.D., 2002, Coll. Math. J., V33, P221, DOI [10.2307/1559033, DOI 10.2307/1559033]

[4] A note on lattice chains and Delannoy numbers [J].

Caughman, John S. ;

Haithcock, Clifford R. ;

Veerman, J. J. P. .

DISCRETE MATHEMATICS, 2008, 308 (12) :2623-2628

[5] A New Generalization of Delannoy Numbers [J].

Dagli, Muhammet Cihat .

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2020, 51 (04) :1729-1735

[6]

Fray R.D., 1973, J. Comb. Theory, Ser. A, V14, P21, DOI [10.1016/0097-3165(73)90060-5, DOI 10.1016/0097-3165(73)90060-5]

[7] WEIGHTED LATTICE PATHS [J].

FRAY, RD ;

ROSELLE, DP .

PACIFIC JOURNAL OF MATHEMATICS, 1971, 37 (01) :85-&

[8] Proof of Sun's conjectures on integer-valued polynomials [J].

Guo, Victor J. W. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 444 (01) :182-191

[9] On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers [J].

Ipek, Ahmet ;

Ari, Kamil .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 229 :433-439

[10] Some congruences on Delannoy numbers and Schroder numbers [J].

Liu, Ji-Cai ;

Li, Long ;

Wang, Su-Dan .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (07) :2035-2041

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