0,2

Or, largest size of an n-dimensional capset (i.e. a subset of (Z/3Z)^n that does not contain any lines {a, a+r, a+2r}). - Terence Tao (tao(AT)math.ucla.edu), Feb 20 2009

Asymptotically, a(n) = O(3^n/n) and a(n) > (2.21...)^n. - Terence Tao (tao(AT)math.ucla.edu), Feb 20 2009

Apparently equivalent to a problem studied by Abello - see reference.

James Abello (DIMACS, Rutgers), The majority rule and combinatorial geometry (via the symmetric group), preprint, 2004.

Ben Davis and Diane Maclagan, The card game Set. The Mathematical Intelligencer, 25, No. 3, 2003, 33-40.

B. Monjardet, Acyclic domains of linear orders: a survey, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160. [From N. J. A. Sloane (njas(AT)research.att.com), Feb 07 2009]

Aaron Potechin: Maximal caps in AG(6, 3), Designs, Codes and Cryptography, Volume 46, Number 3 / March, 2008

Brink, D. V., 1997, The search for SET

B. Davis and D. Maclagan, The Card Game SET, The Mathematical Intelligencer, Vol. 25:3 (Summer 2003), pp. 33-40.

Yves Edel, Home page

Guardians of SET, SET Home Page

Ivars Peterson, SET Math.

SET card game, Official web site

Terence Tao, Bounds for the first few density Hales-Jewett numbers, and related quantities [From Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 20 2009]

Zabrocki, M., 2001, The Joy of SET

B. L. Davis and D. Maclagan, The Card Game SET [From Omar E. Pol (info(AT)polprimos.com), Feb 21 2009]

Ivars Peterson, SET Math [From Omar E. Pol (info(AT)polprimos.com), Feb 21 2009]

Bounded above by the sequence A003142. Cf. A090246, A156989.

Sequence in context: A167750 A111099 A000632 this_sequence A006958 A036617 A007902

Adjacent sequences: A090242 A090243 A090244 this_sequence A090246 A090247 A090248

hard,more,nonn,nice

Hans Havermann (pxp(AT)rogers.com), Jan 23 2004

a(6) sent by Terence Tao (tao(AT)math.ucla.edu), Feb 20 2009

Edited by N. J. A. Sloane, Feb 21 2009