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A283113
Triangle read by rows: T(n,k) is the number of nonequivalent ways (mod D_3) to place k points on an n X n X n triangular grid so that no two of them are on the same row, column or diagonal (n >= 1).
6
1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 9, 5, 1, 5, 19, 23, 3, 1, 7, 38, 82, 40, 1, 1, 8, 66, 230, 242, 45, 1, 10, 110, 560, 1038, 533, 29, 1, 12, 170, 1208, 3504, 3546, 821, 6, 1, 14, 255, 2392, 9998, 16917, 9137, 807, 1, 16, 365, 4405, 25158, 64345, 63755, 17408, 422
OFFSET
1,6
COMMENTS
Length of n-th row is A004396(n) + 1, for 1 <= n <= 21, where A004396(n) is the maximal number of points that can be placed under the condition mentioned above.
Rotations and reflections of placements are not counted. If they are to be counted, see A193986.
In terms or triangular chess: Number of nonequivalent ways (mod D_3) to arrange k nonattacking rooks on an n X n X n board, k>=0, n>=1.
LINKS
EXAMPLE
The table begins with T(1,0), T(1,1);
1, 1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 9, 5;
1, 5, 19, 23, 3;
1, 7, 38, 82, 40, 1;
1, 8, 66, 230, 242, 45;
1, 10, 110, 560, 1038, 533, 29;
...
CROSSREFS
Row sums give A283117.
Sequence in context: A297020 A099597 A358146 * A123610 A209631 A309876
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, Mar 10 2017
STATUS
approved