OFFSET
1,8
COMMENTS
Computed by Tom Duff, Jun 15 2020
For the limiting probability that the four points form a convex quadrilateral when n and k are large, see the link to Sylvester's Four-Point Problem. Thanks to Ed Pegg Jr for this comment.
LINKS
Eric Weisstein's World of Mathematics, Sylvester's Four-Point Problem.
EXAMPLE
The initial rows of the array are:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, ...
0, 9, 70, 276, 750, 1677, 3260, 5776, 9508, 14825, 22090, 31764, ...
0, 36, 276, 1038, 2788, 6190, 11942, 21062, 34586, 53748, 79930, 114760, ...
0, 100, 750, 2788, 7398, 16328, 31396, 55244, 90484, 140372, 208490, 299048, ...
0, 225, 1677, 6190, 16328, 35727, 68447, 120106, 196338, 304161, 451035, 646116, ...
0, 441, 3260, 11942, 31396, 68447, 130768, 229034, 373968, 578777, 857524, 1227572, ...
0, 784, 5776, 21062, 55244, 120106, 229034, 400116, 652318, 1008438, 1492870, 2135534, ...
0, 1296, 9508, 34586, 90484, 196338, 373968, 652318, 1062016, 1640284, 2426660, 3469356, ...
0, 2025, 14825, 53748, 140372, 304161, 578777, 1008438, 1640284, 2531001, 3742053, 5347100, ...
...
The initial antidiagonals are:
0,
0, 0,
0, 1, 0,
0, 9, 9, 0,
0, 36, 70, 36, 0,
0, 100, 276, 276, 100, 0,
0, 225, 750, 1038, 750, 225, 0,
0, 441, 1677, 2788, 2788, 1677, 441, 0,
0, 784, 3260, 6190, 7398, 6190, 3260, 784, 0,
0, 1296, 5776, 11942, 16328, 16328, 11942, 5776, 1296, 0,
0, 2025, 9508, 21062, 31396, 35727, 31396, 21062, 9508, 2025, 0,
0, 3025, 14825, 34586, 55244, 68447, 68447, 55244, 34586, 14825, 3025, 0,
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 15 2020
STATUS
approved