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A243211 Triangle T(n, k) = Numbers of 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, 3, 3, 1, 6, 15, 15, 3, 1, 10, 45, 107, 128, 63, 10, 1, 15, 105, 428, 1062, 1566, 1276, 507, 69, 1, 21, 210, 1282, 5160, 13971, 25191, 29235, 20508, 7747, 1251, 42, 1, 1, 28, 378, 3198, 18591, 77124, 231090, 498097, 759117, 792942, 540361, 222597, 49053 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The triangle T(n, k) is irregularly shaped: 0 <= 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..165

EXAMPLE

The triangle begins:

  1,  1;

  1,  3,   3;

  1,  6,  15,   15,    3;

  1, 10,  45,  107,  128,    63,    10,

  1, 15, 105,  428, 1062,  1566,  1276,   507,    69,

  1, 21, 210, 1282, 5160, 13971, 25191, 29235, 20508, 7747, 1251, 42, 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, A243207, A084546, A234251, A239567, A240439, A194136, A000217 (column 2), A050534 (column 3), A243212 (column 4), A243213 (column 5), A243214 (column 6).

Sequence in context: A278390 A001498 A240439 * A199034 A138464 A117279

Adjacent sequences:  A243208 A243209 A243210 * A243212 A243213 A243214

KEYWORD

nonn,tabf

AUTHOR

Heinrich Ludwig, Jun 09 2014

STATUS

approved

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)