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 A243207 Triangle T(n, k) = Numbers of inequivalent (mod D_3) ways to place k points on a triangular grid of side n so that no three of them are vertices of an equilateral triangle with sides parallel to the grid. Triangle read by rows. 5
 1, 1, 1, 2, 4, 3, 1, 3, 10, 20, 25, 11, 3, 4, 22, 77, 186, 266, 221, 86, 14, 5, 41, 223, 881, 2344, 4238, 4885, 3451, 1296, 220, 7, 1, 7, 72, 552, 3146, 12907, 38640, 83107, 126701, 132236, 90214, 37128, 8235, 775, 24, 8, 116, 1196, 9264, 53307, 232861, 773930 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The triangle T(n, k) is irregularly shaped: 1 <= k <= A227308(n). First row corresponds to n = 1. The maximal number of points that can be placed on a triangular grid of side n so that no three of them form an equilateral triangle with sides parallel to the grid is given by A227308(n). LINKS Heinrich Ludwig, Table of n, a(n) for n = 1..153 EXAMPLE The triangle begins: 1; 1, 1; 2, 4, 3, 1; 3, 10, 20, 25, 11, 3; 4, 22, 77, 186, 266, 221, 86, 14; 5, 41, 223, 881, 2344, 4238, 4885, 3451, 1296, 220, 7, 1; ... There is T(6, 12) = 1 way to place 12 points (x) on the grid obeying the rule in the definition of the sequence: . x x x . x x . . x x . . . x . x x x x . CROSSREFS Cf. A227308, A243211, A239572, A234247, A231655, A243141, A001399 (column 1), A227327 (column 2), A243208 (column 3), A243209 (column 4), A243210 (column 5). Sequence in context: A347270 A275117 A243141 * A297003 A071284 A104753 Adjacent sequences: A243204 A243205 A243206 * A243208 A243209 A243210 KEYWORD tabf,nonn AUTHOR Heinrich Ludwig, Jun 01 2014 STATUS approved

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Last modified August 7 15:23 EDT 2024. Contains 375017 sequences. (Running on oeis4.)