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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 November 14 11:04 EST 2018. Contains 317182 sequences. (Running on oeis4.)