

A243207


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 with sides parallel to the grid. Triangle read by rows.


5



1, 1, 1, 2, 4, 3, 1, 3, 10, 20, 25, 11, 3, 4, 22, 77, 186, 266, 221, 86, 14, 5, 41, 223, 881, 2344, 4238, 4885, 3451, 1296, 220, 7, 1, 7, 72, 552, 3146, 12907, 38640, 83107, 126701, 132236, 90214, 37128, 8235, 775, 24, 8, 116, 1196, 9264, 53307, 232861, 773930
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OFFSET

1,4


COMMENTS

The triangle T(n, k) is irregularly shaped: 1 <= k <= A227308(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 with sides parallel to the grid is given by A227308(n).


LINKS



EXAMPLE

The triangle begins:
1;
1, 1;
2, 4, 3, 1;
3, 10, 20, 25, 11, 3;
4, 22, 77, 186, 266, 221, 86, 14;
5, 41, 223, 881, 2344, 4238, 4885, 3451, 1296, 220, 7, 1;
...
There is T(6, 12) = 1 way to place 12 points (x) on the grid obeying the rule in the definition of the sequence:
.
x x
x . x
x . . x
x . . . x
. x x x x .


CROSSREFS

Cf. A227308, A243211, A239572, A234247, A231655, A243141, A001399 (column 1), A227327 (column 2), A243208 (column 3), A243209 (column 4), A243210 (column 5).


KEYWORD

tabf,nonn


AUTHOR



STATUS

approved



