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A240439 Triangle T(n, k) = Numbers of 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. 6
1, 1, 1, 3, 3, 1, 6, 15, 15, 3, 1, 10, 45, 105, 114, 39, 3, 1, 15, 105, 420, 969, 1194, 654, 102, 3, 1, 21, 210, 1260, 4773, 11259, 15615, 11412, 3663, 342, 15, 1, 28, 378, 3150, 17415, 64776, 159528, 250233, 234609, 119259, 28395, 2613, 69, 1, 36, 630, 6930 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
The triangle T(n, k) is irregularly shaped: 0 <= 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, 3, 3;
1, 6, 15, 15, 3;
1, 10, 45, 105, 114, 39, 3;
1, 15, 105, 420, 969, 1194, 654, 102, 3;
1, 21, 210, 1260, 4773, 11259, 15615, 11412, 3663, 342, 15;
There are T(5, 8) = 3 ways to place 8 points (x) on a triangular grid of side 5 under the conditions mentioned above:
. x x
x x x . . x
x . x x . . . . x
x . . x x . . . . . . x
x . . . x . x x x x x x x x .
CROSSREFS
column 2 is A000217,
column 3 is A050534,
column 4 is A240440,
column 5 is A240441,
column 6 is A240442.
Sequence in context: A278390 A356916 A001498 * A243211 A199034 A138464
KEYWORD
nonn,tabf
AUTHOR
Heinrich Ludwig, Apr 05 2014
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)