Delannoy and tetrahedral numbers

J. Schröder

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 3, page 389-394
  • ISSN: 0010-2628

Abstract

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We establish an identity between Delannoy numbers and tetrahedral numbers of arbitrary dimension.

How to cite

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Schröder, J.. "Delannoy and tetrahedral numbers." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 389-394. <http://eudml.org/doc/250227>.

@article{Schröder2007,
abstract = {We establish an identity between Delannoy numbers and tetrahedral numbers of arbitrary dimension.},
author = {Schröder, J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Delannoy numbers; tetrahedral numbers; king's walk; coordination number; crystal ball; Delannoy numbers; tetrahedral numbers; king's walk; coordination number; crystal ball},
language = {eng},
number = {3},
pages = {389-394},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Delannoy and tetrahedral numbers},
url = {http://eudml.org/doc/250227},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Schröder, J.
TI - Delannoy and tetrahedral numbers
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 3
SP - 389
EP - 394
AB - We establish an identity between Delannoy numbers and tetrahedral numbers of arbitrary dimension.
LA - eng
KW - Delannoy numbers; tetrahedral numbers; king's walk; coordination number; crystal ball; Delannoy numbers; tetrahedral numbers; king's walk; coordination number; crystal ball
UR - http://eudml.org/doc/250227
ER -

References

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  1. Aigner M., Diskrete Mathematik, Vieweg, Braunschweig, 1993. Zbl1109.05001MR1243412
  2. Banderier C., Schwer S.R., Why Delannoy numbers?, J. Statist. Plann. Inference 135 1 (2005), 40-54; CoRR math.CO/0411128: (2004). (2005) Zbl1074.01012MR2202337
  3. Conway J.H., Sloane N.J.A., Low dimensional lattices VII: Coordination sequences, Proc. Royal Soc. London Ser. A 453 (1997), 1966 2369-2389; citeseer.ist.psu.edu/article/conway96lowdimensional.html. (1997) Zbl1066.11505MR1480120
  4. Delannoy H., Emploi de l'échiquier pour la résolution de certains problèmes de probabilités, Association Francaise pour l'Avancement des Sciences, Bordeaux XXIV (1895), 70-90. 
  5. Handbook of Discrete and Combinatorial Mathematics, Eds. K.H. Rosen et al., CRC Press, Boca Raton etc., 2000. Zbl1044.00002MR1725200
  6. Pólya G., Szegö G., Aufgaben und Lehrsätze aus der Analysis, I, Springer, Berlin, 1970. 
  7. Schröder J., Filling boxes densely and disjointly, Comment. Math. Univ. Carolin. 44 1 (2003), 187-196. (2003) Zbl1099.54011MR2045855
  8. Schröder J., Generalized Schröder numbers and the rotation principle, preprint, 2007. MR2346050
  9. Stanley R.P., Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999. Zbl0978.05002MR1676282
  10. Vassilev M., Atanassov K., On Delan [ n ] oy numbers, Annuaire Univ. Sofia Fac. Math. Inform. 81 (1987), 153-162. (1987) MR1291893

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