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A290820
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Side length of the smallest equilateral triangles that have a separated dissection into n equilateral triangles with integer sides, or 0 if no such triangle exists.
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4
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1, 0, 0, 2, 0, 3, 4, 4, 6, 5, 8, 6, 6, 7, 8, 7
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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EXAMPLE
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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:
*
/ \
+ +
/ \
*---+---*
/ \ / \
+ + *---*
/ \ / \ / \
*---*---*---*---*
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---* + + +
/ \ / \ / \
*---*---+---+---*---+---+---*
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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Title changed as suggested by Peter Munn, Feb 17 2018
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STATUS
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approved
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