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A234251 Triangle T(n, k) = Number of ways to choose k points from an n X n X n triangular grid so that no three of them form a 2 X 2 X 2 subtriangle. Triangle T read by rows. 4
1, 1, 1, 3, 3, 1, 6, 15, 16, 6, 1, 10, 45, 111, 156, 120, 42, 2, 1, 15, 105, 439, 1191, 2154, 2583, 1977, 885, 189, 9, 1, 21, 210, 1305, 5565, 17052, 38337, 63576, 77208, 67285, 40512, 15750, 3480, 333, 9, 1, 28, 378, 3240, 19620, 88590, 307362, 833228, 1779219 (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 0 to A007980(n - 1).
Column #2 (k = 1) is A000217.
Column #3 (k = 2) is A050534.
Column #4 (k = 3) is A234250.
LINKS
EXAMPLE
Triangle begins
1, 1;
1, 3, 3;
1, 6, 15, 16, 6;
1, 10, 45, 111, 156, 120, 42, 2;
1, 15, 105, 439, 1191, 2154, 2583, 1977, 885, 189, 9;
...
There are no more than T(4, 7) = 2 ways to choose 7 points (X) from a 4 X 4 X 4 grid so that no 3 of them form a 2 X 2 X 2 subtriangle:
X X
X . . X
. X X X X .
X X . X X . X X
CROSSREFS
Sequence in context: A199034 A138464 A117279 * A049323 A322148 A084144
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, Feb 06 2014
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)