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 A056814 Triangle partitions of order n: topologically distinct ways to dissect a triangle into n triangles. 2
 1, 4, 23, 180, 1806, 20198 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 13 21:44 EDT 2024. Contains 374288 sequences. (Running on oeis4.)