A229757 Numbers n such that no convex hexagon exists that can be dissected into n congruent equilateral triangles.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 17, 20, 21, 23, 29, 36, 39, 41, 44, 84

Offset

1,2

Comments

Numbers not expressible as k = 2*(a*c + b*c + b*d) - (a-d)^2 with a,b,c,d >= 1, a < c+d, d < a+b.

See the Hertel paper for the finiteness proof.

Links

Table of n, a(n) for n=1..21.

Eike Hertel, Reguläre Dreieckspflasterungen konvexer Polygone, Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/13, 2013 (preprint).

Eike Hertel, Christian Richter, Tiling Convex Polygons with Congruent Equilateral Triangles, Discrete Comput Geom (2014) 51:753-759.

Kival Ngaokrajang, Illustration of initial terms

Crossrefs

Cf. A229461 (Pentagon exception numbers).

Sequence in context: A050730 A288221 A346782 * A319272 A366142 A141819

Adjacent sequences: A229754 A229755 A229756 * A229758 A229759 A229760

Keyword

nonn,fini,full

Author

Suggested by Eike Hertel, Hugo Pfoertner, Sep 28 2013

Status

approved