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A167123 Number of isomorphism classes of separated dissections of an equilateral triangle into n nonoverlapping equilateral triangles. 6
1, 0, 0, 1, 0, 1, 2, 3, 8, 20, 55, 161, 478, 1496, 4804, 15589, 51377, 172162, 583810, 1998407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

A dissection into 5 triangles is impossible.

From table on p.11 of Drapal. The authors write: We enumerate all dissections of an equilateral triangle into smaller equilateral triangles. We confirm W. T. Tutte's claim that the smallest perfect dissection has size 15 and we find all perfect dissections up to size 20.

The meaning of "separated dissection" is defined at the end of the introduction of the Drapal and Hamalainen article, see link. - Hugo Pfoertner, Feb 17 2018

LINKS

Table of n, a(n) for n=1..20.

Ales Drapal, Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010.

Stuart Anderson, An Introduction to Triangled Equilateral Triangles.

EXAMPLE

a(8)=3:

            *

           / \

          /   \

         /     \

        /       \

       /         \

      *---*-------*

     / \ / \     / \

    *---*   \   /   \

   / \ /     \ /     \

  *---*-------*-------*

            *

           / \

          /   \

         /     \

        *-------*

       / \     / \

      *---*   /   \

     / \ / \ /     \

    /   *---*       \

   /     \ /         \

  *-------*-----------*

          *

         / \

        *---*

       / \ / \

      *---*   \

     / \ /     \

    *---*       \

   / \ /         \

  *---*-----------*

CROSSREFS

Cf. A290653, A290697, A299705.

Sequence in context: A333680 A254533 A095341 * A029895 A073268 A073190

Adjacent sequences:  A167120 A167121 A167122 * A167124 A167125 A167126

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Oct 27 2009

EXTENSIONS

a(1)-a(3) added and name accommodated as suggested by M. F. Hasler, Feb 23 2018

Corrected and extended by Hugo Pfoertner, Aug 09 2017

Definition corrected by Hugo Pfoertner, Feb 17 2018

STATUS

approved

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Last modified May 25 06:43 EDT 2022. Contains 354049 sequences. (Running on oeis4.)