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A243141
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 of any orientation. Triangle read by rows.
5
1, 1, 1, 2, 4, 3, 1, 3, 10, 19, 22, 7, 1, 4, 22, 75, 170, 204, 115, 18, 1, 5, 41, 218, 816, 1891, 2635, 1909, 628, 58, 3, 7, 72, 542, 2947, 10846, 26695, 41770, 39218, 19905, 4776, 437, 13, 8, 116, 1178, 8765, 46068, 171700, 444117, 776276, 876012, 601078, 229941
OFFSET
1,4
COMMENTS
The triangle T(n, k) is irregularly shaped: 1 <= k <= A240114(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 is given by A240114(n).
LINKS
EXAMPLE
The triangle begins:
1;
1, 1;
2, 4, 3, 1;
3, 10, 19, 22, 7, 1;
4, 22, 75, 170, 204, 115, 18, 1;
5, 41, 218, 816, 1891, 2635, 1909, 628, 58, 3;
7, 72, 542, 2947, 10846, 26695, 41770, 39218, 19905, 4776, 437, 13;
...
There is exactly T(5, 8) = 1 way to place 8 points (x) on a triangular grid of side 5 according to the definition of the sequence:
.
x x
x . x
x . . x
x . . . x
CROSSREFS
Cf. A240114, A240439, A001399 (column 1), A227327 (column 2), A243142 (column 3), A243143 (column 4), A243144 (column 5).
Sequence in context: A125941 A347270 A275117 * A243207 A297003 A071284
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, May 30 2014
STATUS
approved