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%I #34 May 13 2019 11:26:17
%S 1,0,0,1,0,1,2,3,8,20,55,161,478,1496,4804,15589,51377,172162,583810,
%T 1998407
%N Number of isomorphism classes of separated dissections of an equilateral triangle into n nonoverlapping equilateral triangles.
%C A dissection into 5 triangles is impossible.
%C 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.
%C 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
%H Ales Drapal, Carlo Hamalainen, <a href="http://arxiv.org/abs/0910.5199">An enumeration of equilateral triangle dissections</a>, arXiv:0910.5199 [math.CO], 2009-2010.
%H Stuart Anderson, <a href="http://web.archive.org/web/20170806090944/http://www.squaring.net/tri/tritri/tet.html">An Introduction to Triangled Equilateral Triangles.
%e a(8)=3:
%e *
%e / \
%e / \
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%e / \
%e / \
%e *---*-------*
%e / \ / \ / \
%e *---* \ / \
%e / \ / \ / \
%e *---*-------*-------*
%e *
%e / \
%e / \
%e / \
%e *-------*
%e / \ / \
%e *---* / \
%e / \ / \ / \
%e / *---* \
%e / \ / \
%e *-------*-----------*
%e *
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%e *---*
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%e *---* \
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%e *---* \
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%e *---*-----------*
%Y Cf. A290653, A290697, A299705.
%K nonn
%O 1,7
%A _Jonathan Vos Post_, Oct 27 2009
%E a(1)-a(3) added and name accommodated as suggested by _M. F. Hasler_, Feb 23 2018
%E Corrected and extended by _Hugo Pfoertner_, Aug 09 2017
%E Definition corrected by _Hugo Pfoertner_, Feb 17 2018
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