OFFSET
1,4
COMMENTS
No solution exists for n = [2, 3, 5].
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
Stuart Anderson, An Introduction to Triangled Equilateral Triangles
Ales Drapal and Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010.
Hugo Pfoertner, Illustration for a(16)=7.
EXAMPLE
a(6) = 3:
*
/ \
*---*
/ \ / \
*---* +
/ \ / \
*---*---+---*
a(7) = 4:
*
/ \
+ +
/ \
*---*---*
/ \ / \ / \
+ *---* +
/ \ / \
*---+---*---+---*
a(8) = 4:
*
/ \
*---*
/ \ / \
*---* +
/ \ / \
*---* +
/ \ / \
*---*---+---+---*
a(9) = 6:
*
/ \
+ +
/ \
*---+---*
/ \ / \
+ + + +
/ \ / \
*---+---* +
/ \ / \
*---* + +
/ \ / \ / \
*---*---*---+---+---+---*
a(10) = 5:
*
/ \
*---*
/ \ / \
*---* +
/ \ / \
*---* +
/ \ / \
*---* +
/ \ / \
*---*---+---+---+---*
a(11) = 8:
*
/ \
+ +
/ \
*---+---*
/ \ / \
+ + + +
/ \ / \
*---+---* +
/ \ / \
+ + + +
/ \ / \
*---+---* +
/ \ / \
*---* + +
/ \ / \ / \
*---*---*---+---+---+---+---+---*
a(12) = 6:
*
/ \
*---*
/ \ / \
*---* +
/ \ / \
*---* +
/ \ / \
*---* +
/ \ / \
*---* +
/ \ / \
*---*---+---+---+---+---*
a(13) = 6:
*
/ \
+ +
/ \
*---+---*
/ \ / \
+ + *---*
/ \ / \ / \
*---*---*---* +
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---*---+---*---+---+---*
a(14) = 7:
*
/ \
+ +
/ \
+ +
/ \
*---+---*---*
/ \ / \ / \
+ + *---* +
/ \ / \ / \
*---*---*---* +
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---*---+---*---+---+---+---*
a(15) = 8:
*
/ \
+ +
/ \
*---+---*
/ \ / \
+ + *---*
/ \ / \ / \
+ *---* +
/ \ / \
*---+---+---* +
/ \ / \
*---* + +
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---*---+---*---+---+---+---+---*
a(16) = 7:
*
/ \
+ +
/ \
*---+---*
/ \ / \
+ + *---*
/ \ / \ / \
*---*---*---*---*
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---*---+---+---*---+---+---*
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Hugo Pfoertner, Aug 11 2017
EXTENSIONS
Title changed as suggested by Peter Munn, Feb 17 2018
STATUS
approved