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A227116 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. 8
0, 1, 2, 4, 7, 9, 14, 18, 23, 29, 36, 44, 52, 61, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This is the complementary problem to A227308.
Numbers found by an exhaustive computational search for all solutions (see history).
LINKS
FORMULA
a(n) + A227308(n) = n(n+1)/2.
EXAMPLE
n = 11: at least a(11) = 36 points (.) out of the 66 have to be removed, leaving 30 (X) behind:
.
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.
CROSSREFS
Sequence in context: A090893 A100486 A139533 * A180742 A039904 A115162
KEYWORD
nonn,hard,more
AUTHOR
Heinrich Ludwig, Jul 01 2013
EXTENSIONS
Added a(12), a(13), Heinrich Ludwig, Sep 02 2013
Added a(14), Giovanni Resta, Sep 19 2013
a(15) from Heinrich Ludwig, Oct 27 2013
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)