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A234350
Triangle T(n, k) = Number of non-equivalent (mod D_3) ways to arrange k indistinguishable points on a triangular grid of side n so that no three points are collinear. Triangle read by rows.
6
1, 1, 1, 1, 2, 4, 5, 2, 3, 10, 22, 24, 8, 1, 4, 22, 77, 153, 140, 47, 2, 5, 41, 217, 713, 1290, 1112, 322, 15, 7, 72, 530, 2557, 7374, 11743, 8783, 2412, 143, 1, 8, 116, 1149, 7661, 32477, 82988, 116154, 77690, 19621, 1220, 5, 10, 180, 2288, 20055, 116420, 433372
OFFSET
1,5
COMMENTS
The triangle T(n, k) is irregularly shaped: 1 <= k <= A234349(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 points are collinear is given by A234349(n).
Without the restriction "non-equivalent (mod D_3)" the numbers are given by A194136.
LINKS
EXAMPLE
Triangle begins
1;
1, 1, 1;
2, 4, 5, 2;
3, 10, 22, 24, 8, 1;
4, 22, 77, 153, 140, 47, 2;
5, 41, 217, 713, 1290, 1112, 322, 15;
7, 72, 530, 2557, 7374, 11743, 8783, 2412, 143, 1;
8, 116, 1149, 7661, 32477, 82988, 116154, 77690, 19621, 1220, 5;
...
There are e.g. T(8, 11) = 5 non-equivalent ways to arrange 11 indistinguishable points (X) on a triangular grid of side 8 so that no point triple is collinear. As examples of the 5 solutions the 2 symmetrical ones are shown.
. .
. . . .
. X . . X .
X . . X X . . X
X . . . X . X . X .
. . X X . . X . . . . X
. X . . . X . . . X . X . .
. . X . . X . . . . X . . X . .
CROSSREFS
Row lengths are given by A234349
Column 1 is A001399
Column 2 is A227327 for n >= 2
Column 3 is A234351
Column 4 is A234352
Column 5 is A234353
Column 6 is A234354.
Sequence in context: A369772 A059215 A125142 * A324035 A096352 A260720
KEYWORD
nonn,tabf,nice
AUTHOR
Heinrich Ludwig, Dec 24 2013
STATUS
approved