A229757 - OEIS

%I #14 Jul 14 2019 05:24:28

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

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

%C 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.

%C See the Hertel paper for the finiteness proof.

%H Eike Hertel, <a href="http://www.minet.uni-jena.de/preprints/hertel_13/Regdreipfla.pdf">Reguläre Dreieckspflasterungen konvexer Polygone</a>, Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/13, 2013 (preprint).

%H Eike Hertel, Christian Richter, <a href="https://doi.org/10.1007/s00454-014-9576-7">Tiling Convex Polygons with Congruent Equilateral Triangles</a>, Discrete Comput Geom (2014) 51:753-759.

%H Kival Ngaokrajang, <a href="/A229757/a229757.pdf">Illustration of initial terms</a>

%Y Cf. A229461 (Pentagon exception numbers).

%K nonn,fini,full

%O 1,2

%A Suggested by Eike Hertel, _Hugo Pfoertner_, Sep 28 2013