

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.


5



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], 20092010.


EXAMPLE

a(11)=7:
*
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ 7 \
/ \
/ \
/ \
***
/ \ / \ / \
/ \ 3 / \ / \
/ 2 \ / \ 4 / \
** / \ / \
/ \ 2 / \ / 4 \ / 4 \
/ \ ** \ / \
/ 2 \ / \ / \ / \
*****
More illustrations are provided on pages 1719 of the Drapal and Hamalainen article.


CROSSREFS

Cf. A167123, A290653.
Sequence in context: A134816 A228361 A182097 * A290821 A072493 A064324
Adjacent sequences: A290694 A290695 A290696 * A290698 A290699 A290700


KEYWORD

nonn,hard,more


AUTHOR

Hugo Pfoertner, Aug 09 2017


STATUS

approved



