Losanitsch’s triangle

A triangular arrangement of numbers very similar to Pascal’s triangle.

Begin as you would if you were constructing Pascal’s triangle, with a 1 in the top row, and that row k numbered 0, and the 1’s position n as 0.


Now, for the next value, add up the two values above, but then subtract


From this forward, do the same for every even-numbered position in an even-numbered row. Instead of calculating the binomial coefficientDlmfDlmfMathworldPlanetmath, it can be looked up in Pascal’s triangle.


This triangle was first studied by the Serbian chemist Sima Losanitsch, but has since been found to have applications in graph theoryMathworldPlanetmath and combinatoricsDlmfMathworld.


  • 1 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
Title Losanitsch’s triangle
Canonical name LosanitschsTriangle
Date of creation 2013-03-22 15:44:09
Last modified on 2013-03-22 15:44:09
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 13
Author CompositeFan (12809)
Entry type Definition
Classification msc 05C38
Synonym Lozanic’s triangle
Synonym Lozanić’s triangle