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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 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 / \ *-------* / \ / \ / \ 2 / \ / 4 \ / 4 \ / \ *---* \ / \ / 2 \ / \ / \ / \ *-------*---*---------------*---------------* More illustrations are provided on pages 17-19 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

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