A003142 Largest subset of 3 X 3 X ... X 3 cube (in n dimensions) with no 3 points collinear. (Formerly M1611)

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

Offset

0,2

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

Ashok K. Chandra, On the Solution of Moser's Problem in Four Dimensions, Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 507 - 511 [DOI: https://doi.org/10.4153/CMB-1973-082-3]

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

Links

Table of n, a(n) for n=0..6.

Thomas Bloom, Problem 185, Erdős Problems.

Václav Chvátal, Edmonds polytopes and a hierarchy of combinatorial problems, Discr. Math. 4 (1973) no 4, 305-337.

Erdős problems database contributors, Erdős problem database, see no. 185.

Kevin O'Bryant, Sets of Natural Numbers with Proscribed Subsets, J. Int. Seq. 18 (2015) # 15.7.7.

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

Crossrefs

Sequence in context: A295572 A372191 A027068 * A335686 A118041 A105073

Adjacent sequences: A003139 A003140 A003141 * A003143 A003144 A003145

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Status

approved