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A227116
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Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be removed from the grid, so that, if 3 of the remaining points are chosen, they do not form an equilateral triangle with sides parallel to the grid.
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8
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0, 1, 2, 4, 7, 9, 14, 18, 23, 29, 36, 44, 52, 61, 71
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OFFSET
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1,3
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COMMENTS
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This is the complementary problem to A227308.
Numbers found by an exhaustive computational search for all solutions (see history).
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LINKS
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FORMULA
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EXAMPLE
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n = 11: at least a(11) = 36 points (.) out of the 66 have to be removed, leaving 30 (X) behind:
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X X
X . X
X . . X
X . . . X
X . . . . X
. X X . X X .
. X . X X . X .
. . X X . X X . .
X . . . . . . . . X
. X X X . . . X X X .
There is no equilateral subtriangle with all vertices = X and sides parallel to the whole triangle.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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