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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 (list; graph; refs; listen; history; text; internal format)
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
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 / \
*-------* / \ / \
/ \ 2 / \ / 4 \ / 4 \
/ \ *---* \ / \
/ 2 \ / \ / \ / \
*-------*---*---------------*---------------*
More illustrations are provided on pages 17-19 of the Drapal and Hamalainen article.
CROSSREFS
Sequence in context: A134816 A228361 A182097 * A290821 A072493 A064324
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Aug 09 2017
STATUS
approved

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Last modified February 21 04:08 EST 2024. Contains 370219 sequences. (Running on oeis4.)