On an extremal problem related to the Delannoy numbers

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

1. Comtet, L. Advanced Combinatorics, D. Reidel Publ. Co. Dordrecht, 1974.
2. 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.