A229757 - OEIS

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

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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

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.

CROSSREFS

Cf. A229461 (Pentagon exception numbers).

KEYWORD

nonn,fini,full

AUTHOR

Suggested by Eike Hertel, Hugo Pfoertner, Sep 28 2013

STATUS

approved