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A086676 Number of n-dimensional 2 X 2 X ... X 2 grid graphs needed to cover an n-dimensional 3 X 3 X ... X 3 torus. 1

%I

%S 2,3,5,8,12,18,29,44,68

%N Number of n-dimensional 2 X 2 X ... X 2 grid graphs needed to cover an n-dimensional 3 X 3 X ... X 3 torus.

%D Patric R. J. Östergård and T. Riihonen, A covering problem for tori, Annals of Combinatorics, 7 (2003), 1-7.

%H D. Brink, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Brink/brink3.html">The Inverse Football Pool Problem</a>, J. Int. Seq. 14 (2011) # 11.8.8.

%H Emil Kolev, <a href="http://www.moi.math.bas.bg/acct2014/a33.pdf">Covering of {F_3}^n with spheres of maximal radius</a>, Fourteenth International Workshop on Algebraic and Combinatorial Coding Theory, September 7-13, 2014, Svetlogorsk (Kaliningrad region), Russia pp. 198-203.

%H E. Kolev and T. Baicheva, <a href="http://www.moi.math.bas.bg/oc2013/a21.pdf">About the inverse football pool problem for 9 games</a>, Seventh International Workshop on Optimal Codes and Related Topics, September 6-12, 2013, Albena, Bulgaria pp. 125-133.

%H Patric R. J. Östergård, <a href="https://users.aalto.fi/~pat/">Home page</a>

%e Known bounds for n=10 through 13, from Kolev (2014):

%e 10 102-104

%e 11 153-172

%e 12 230-264

%e 13 345-408

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 28 2003

%E I have added two terms (29 and 44). The ranges for the next terms are [66,68] and [99,104]. _David Brink_, Jun 03 2009

%E For a(9) = 68 and further bounds see Kolev and Baicheva. - _N. J. A. Sloane_, Mar 10 2014

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Last modified August 18 09:28 EDT 2022. Contains 356204 sequences. (Running on oeis4.)