A003142 Largest subset of 3 X 3 X ... X 3 cube (in n dimensions) with no 3 points collinear.

0, 2, 6, 16, 43, 124, 353

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

The D. H. J. Polymath collective found a(5) and a(6) and gives the bound a(n) >= (2 + o(1))*binomial(n, i)*2^i for any i (and note that this is maximized by i near 2n/3). - Charles R Greathouse IV, Jun 11 2013

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• K. O'Bryant, Sets of Natural Numbers with Proscribed Subsets, J. Int. Seq. 18 (2015) # 15.7.7.
• V. Chvatal, Edmonds polytopes and a hierarchy of combinatorial problems, Discr. Math. 4 (1973) no 4, 305-337.
• D. H. J. Polymath, Density Hales-Jewett and Moser numbers, arXiv:1002.0374 [math.CO], 2010.
• Index entries for sequences related to tic-tac-toe