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A234247 Triangle T(n,k) read by rows: Number of non-equivalent ways (mod D_3) to choose k points from an nXnXn triangular grid so that no three of them form a 2X2X2 subtriangle. 3
1, 1, 1, 2, 4, 4, 2, 3, 10, 22, 31, 22, 10, 1, 4, 22, 82, 212, 374, 450, 342, 156, 36, 2, 5, 41, 231, 955, 2880, 6459, 10660, 12948, 11274, 6802, 2645, 595, 57, 2, 7, 72, 566, 3335, 14883, 51470, 139224, 297048, 500147, 661796, 681101, 536322, 314753, 132490 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

n starts from 1. The maximal number of points that can be chosen from a grid of side n, so that no three of them are forming a subtriangle of side 2, is A007980(n - 1). So k ranges from 1 to A007980(n - 1).

Column #1 (k = 1) is A001399.

Column #2 (k = 2) is A227327.

Without the restriction "non-equivalent (mod D_3)" numbers are given by A234251.

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 1..123

EXAMPLE

Triangle begins

1;

1,  1;

2,  4,   4,   2;

3, 10,  22,  31,   22,   10,     1;

4, 22,  82, 212,  374,  450,   342,   156,    36,    2;

5, 41, 231, 955, 2880, 6459, 10660, 12948, 11274, 6802, 2645, 595, 57, 2;

...

There are exactly T(5, 10) = 2 non-equivalent ways to choose 10 points (X) from a triangular grid of side 5 avoiding that any three of them form a subtriangle of side 2.

       .                X

      X X              . X

     X . X            X . X

    . X X .          . X X .

   X X . X X        X X . X X

CROSSREFS

Cf. A234251, A007980, A001399, A227327.

Sequence in context: A256066 A096832 A016588 * A160163 A263442 A206396

Adjacent sequences:  A234244 A234245 A234246 * A234248 A234249 A234250

KEYWORD

nonn,tabf

AUTHOR

Heinrich Ludwig, Feb 11 2014

STATUS

approved

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Last modified November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)