Mladen Vassilev-Missana and Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 14, 2008, Number 2, Pages 11—14
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Mladen Vassilev-Missana
Krassimir Atanassov
Abstract
In the paper the maximal elements of the set {D(n − k, k | k = 0, 1, …, n} are found, where D(p, q) are the so-called Delannoy numbers and n ≥ 2 is a natural number. It is shown that for an even n the number D(n/2, n/2) is the maximal element of the mentioned set, while when n is odd – the maximal elements are two D([n/2]+1, [n/2]) and D([n/2], [n/2]+1).
References
- Comtet, L. Advanced Combinatorics, D. Reidel Publ. Co. Dordrecht, 1974.
- Vassilev M., Atanassov K., On Delanoy numbers, Annuaire de l’Universite de Sofia “St. Kliment Ohridski”, Faculte de Mathematiques et Informatique, Livre 1 – Mathematiques, Tome 81, 1987, 153-162.
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Vassilev-Missana, M., & Atanassov, K. (2008). On an extremal problem related to the Delannoy numbers. Notes on Number Theory and Discrete Mathematics, 14(2), 11-14.