A056814 Triangle partitions of order n: topologically distinct ways to dissect a triangle into n triangles.

1, 4, 23, 180, 1806, 20198

Offset

2,2

Links

Table of n, a(n) for n=2..7.

Ed Pegg, Jr., Triangles

Z. Skupien, A. Zak, Pair-sums 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 131-144, (in English and Russian).

Miroslav Vicher, Triangle Partitions

Eric Weisstein's World of Mathematics, Triangle Dissection

Example

From M. F. Hasler, Feb 15 2024: (Start)
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

Cf. A053740.

Sequence in context: A089465 A220214 A106174 * A058863 A192840 A302189

Adjacent sequences: A056811 A056812 A056813 * A056815 A056816 A056817

Keyword

nonn,more,nice,hard

Author

N. J. A. Sloane, Sep 01 2000

Status

approved