

A056814


Triangle partitions of order n: topologically distinct ways to dissect a triangle into n triangles.


2




OFFSET

2,2


LINKS

Z. Skupien, A. Zak, Pairsums packing and rainbow cliques, in Topics In Graph Theory, A tribute to A. A. and T. E. Zykovs on the occasion of A. A. Zykov's 90th birthday, ed. R. Tyshkevich, Univ. Illinois, 2013, pages 131144, (in English and Russian).


EXAMPLE

a(2) = 1 because up to equivalence, there is only one partition of a triangle in two smaller ones, using a segment from one vertex to a point on the opposite side. (Here and below, "on" excludes the endpoints.)
a(3) = 4 is the number of partitions of a triangle ABC into three smaller ones: One uses three segments AD, BD and CD, where D is a point inside ABC. Three other topologically inequivalent partitions of order 3 each use two segments, as follows: {AE, AF}, {AE, EG} and {AE, BH}, where E and F are two distinct points on BC, G is a point on AB, and H is a point on AE. (End)


CROSSREFS



KEYWORD

nonn,more,nice,hard


AUTHOR



STATUS

approved



