login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A229757 Numbers n such that no convex hexagon exists that can be dissected into n congruent equilateral triangles. 2
1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 17, 20, 21, 23, 29, 36, 39, 41, 44, 84 (list; graph; refs; listen; history; text; internal format)
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: A079734 A050730 A288221 * A319272 A141819 A097904

Adjacent sequences:  A229754 A229755 A229756 * A229758 A229759 A229760

KEYWORD

nonn,fini,full

AUTHOR

Suggested by Eike Hertel, Hugo Pfoertner, Sep 28 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)