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A290697
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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.
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5
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2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 67, 91
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OFFSET
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6,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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