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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
Ales Drapal, Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010.
EXAMPLE
a(8)=3:
*
/ \
/ \
/ \
/ \
/ \
*---*-------*
/ \ / \ / \
*---* \ / \
/ \ / \ / \
*---*-------*-------*
*
/ \
/ \
/ \
*-------*
/ \ / \
*---* / \
/ \ / \ / \
/ *---* \
/ \ / \
*-------*-----------*
*
/ \
*---*
/ \ / \
*---* \
/ \ / \
*---* \
/ \ / \
*---*-----------*
CROSSREFS
Sequence in context: A333680 A254533 A095341 * A029895 A073268 A073190
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 April 21 19:08 EDT 2024. Contains 371874 sequences. (Running on oeis4.)