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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). REFERENCES Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337.  Solution published in Vol. 29, No. 3, Fall 1995, pp. 324-325. Mohammad K. Azarian, A Trigonometric Characterization of  Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96.  Solution published in Vol. 32, No. 1, Winter 1998, pp. 84-85. LINKS Heinrich Ludwig, Illustration of a(2)..a(15) Ed Wynn, A comparison of encodings for cardinality constraints in a SAT solver, arXiv:1810.12975 [cs.LO], 2018. 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 Cf. A227308, A152125, A227133 Sequence in context: A090893 A100486 A139533 * A180742 A039904 A115162 Adjacent sequences:  A227113 A227114 A227115 * A227117 A227118 A227119 KEYWORD nonn,hard,more,changed 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 January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)