OFFSET
1,7
COMMENTS
Data for n <= 15 from Figure 7 of Drápal and Hämäläinen. The published Figure 7 values for n = 16..20 were undercounts. - Jinwoo Park, Aug 24 2026
LINKS
Aleš Drápal and Carlo Hämäläinen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010. [Gives incorrect a(16)-a(20)]
Carlo Hämäläinen and Jinwoo Park, Corrected counts for n = 16..20 (issue with confirmation by the author), GitHub, Aug 2026.
Hugo Pfoertner and Rainer Rosenthal, Illustration of the 23 dissections into 10 triangles.
EXAMPLE
a(9)=9:
* * *
/ \ / \ / \
*---* + + + +
/ \ / \ / \ / \
*---*---* + + + +
/ \ / \ / \ / \ / \
*---*---*---* + + + +
/ \ / \
*---+---*---+---* *---+---+---*---*
/ \ / \ / \ / \ / \ / \
+ + + + + + + + *---*---*
/ \ / \ / \ / \ / \ / \
+ *---*---* + + + + + + +
/ \ / \ / \ / \ / \ / \
*---+---+---*---*---+---+---* *---+---+---*---+---*---+---*
.
* *---+---+---*---+---+---* *
/ \ \ / \ / / \
+ + + + + + + +
/ \ \ / \ / / \
+ + + *---*---* + + +
/ \ \ / \ / \ / \ / / \
+ + *---*---*---* + +
/ \ \ / / \
*---+---*---+---* + + *---+---*---*---*
/ \ / \ / \ \ / / \ / \ / \ / \
+ + + + *---* + + + + + *---* +
/ \ / \ / \ / \ \ / / \ / \ / \
*---+---*---+---*---*---* * *---+---*---+---*---+---*
.
* *---+---*---*---*---+---* *
/ \ \ / \ / \ / \ / / \
+ + + + *---* + + + +
/ \ \ / \ / \ / / \
*---*---* *---+---*---+---* + +
/ \ / \ / \ \ / / \
*---*---*---* + + *---+---+---*
/ \ / \ \ / / \ / \
+ + + + + + + + + +
/ \ / \ \ / / \ / \
+ + + + + + *---*---* + +
/ \ / \ \ / / \ / \ / \ / \
*---+---+---*---+---+---* * *---*---*---*---+---+---*
CROSSREFS
KEYWORD
nonn,hard,more,changed
AUTHOR
Peter Munn and Hugo Pfoertner, Feb 17 2018
EXTENSIONS
Offset changed, also name to accommodate, following suggestion by M. F. Hasler, Feb 23 2018
a(16)-a(20) corrected by Jinwoo Park, Aug 24 2026
STATUS
approved