cp's OEIS Frontend

A167123 Number of isomorphism classes of separated dissections of an equilateral triangle into n nonoverlapping equilateral triangles.

%I A167123 #36 Jan 08 2025 10:31:56
%S A167123 1,0,0,1,0,1,2,3,8,20,55,161,478,1496,4804,15589,51377,172162,583810,
%T A167123 1998407
%N A167123 Number of isomorphism classes of separated dissections of an equilateral triangle into n nonoverlapping equilateral triangles.
%C A167123 A dissection into 5 triangles is impossible.
%C A167123 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 A167123 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 A167123 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 A167123 Stuart Anderson, <a href="http://web.archive.org/web/20170806090944/http://www.squaring.net/tri/tritri/tet.html">An Introduction to Triangled Equilateral Triangles</a>.
%e A167123 a(8)=3:
%e A167123             *
%e A167123            / \
%e A167123           /   \
%e A167123          /     \
%e A167123         /       \
%e A167123        /         \
%e A167123       *---*-------*
%e A167123      / \ / \     / \
%e A167123     *---*   \   /   \
%e A167123    / \ /     \ /     \
%e A167123   *---*-------*-------*
%e A167123             *
%e A167123            / \
%e A167123           /   \
%e A167123          /     \
%e A167123         *-------*
%e A167123        / \     / \
%e A167123       *---*   /   \
%e A167123      / \ / \ /     \
%e A167123     /   *---*       \
%e A167123    /     \ /         \
%e A167123   *-------*-----------*
%e A167123           *
%e A167123          / \
%e A167123         *---*
%e A167123        / \ / \
%e A167123       *---*   \
%e A167123      / \ /     \
%e A167123     *---*       \
%e A167123    / \ /         \
%e A167123   *---*-----------*
%Y A167123 Cf. A290653, A290697, A299705.
%K A167123 nonn
%O A167123 1,7
%A A167123 _Jonathan Vos Post_, Oct 27 2009
%E A167123 a(1)-a(3) added and name accommodated as suggested by _M. F. Hasler_, Feb 23 2018
%E A167123 Corrected and extended by _Hugo Pfoertner_, Aug 09 2017
%E A167123 Definition corrected by _Hugo Pfoertner_, Feb 17 2018