A290653 Number of perfect dissections of equilateral triangles into n equilateral triangles with integer sides.

2, 2, 6, 23, 64, 181

Offset: 15

Author

Hugo Pfoertner, Aug 08 2017

Keywords

• nonn
• more
• hard

Comments

A perfect dissection has no two triangles of the same side. Triangles of different orientation are counted separately. The computation by A. Drapal and C. Hamalainen proves Tutte's conjecture that the smallest perfect dissection has size 15.

Links

• Ales Drapal and Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010.
• W. T. Tutte, The dissection of equilateral triangles into equilateral triangles, Mathematical Proceedings of the Cambridge Philosophical Society, 44(4), 463-482. doi:10.1017/S030500410002449X
• Stuart Anderson, An Introduction to Triangled Equilateral Triangles.
• Stuart Anderson, Illustration of dissections for n=15.
• Stuart Anderson, Illustration of dissections for n=16.
• Stuart Anderson, Illustration of dissections for n=17.
• Stuart Anderson, Illustration of dissections for n=18.
• Stuart Anderson, Illustration of dissections for n=19.
• Stuart Anderson, Illustration of dissections for n=20.

Crossrefs

Cf. A167123, A290697.