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

2, 2, 6, 23, 64, 181

Offset

15,1

Comments

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

Links

Table of n, a(n) for n=15..20.

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.

Aleš Drápal and Carlo Hämäläinen, 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.

Crossrefs

Cf. A167123, A290697.

Sequence in context: A112478 A184715 A292319 * A138801 A188958 A141902

Adjacent sequences: A290650 A290651 A290652 * A290654 A290655 A290656

Keyword

nonn,more,hard

Author

Hugo Pfoertner, Aug 08 2017

Status

approved