A290697 - OEIS

A290697

Size of largest triangle occurring in any of the possible dissections of an equilateral triangle into n equilateral triangles with integer sides, assuming gcd(s_1,s_2,...,s_n)=1, s_k being the side lengths.

2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 67, 91

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OFFSET

6,1

COMMENTS

a(4)=1. A dissection into 5 triangles is impossible.

The size of the smallest triangle is 1 for triangles with maximum ratio of sizes between largest and smallest triangle for all n <= 20. If dissections with maximum size of largest occurring triangle and size of smallest triangle > 1 are found for larger n, there might be different configurations leading to a maximum ratio between largest and smallest side having a shorter largest side than the one provided as a(n). If this situation occurs for any n > 20, it shall be indicated in a corresponding comment.

LINKS

Table of n, a(n) for n=6..20.

Ales Drapal, Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010.

EXAMPLE

a(11)=7:

/ \

/ 7 \

/ \

*-----------*---------------*

/ \ / \ / \

/ \ 3 / \ / \

/ 2 \ / \ 4 / \