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 A213418 T(n,k) = Half the number of n X k binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I. 7

%I #12 Jun 26 2015 11:22:24

%S 1,2,2,4,8,4,8,32,32,8,16,128,253,128,16,32,512,1970,1970,512,32,64,

%T 2048,15109,28952,15109,2048,64,128,8192,114302,407498,407498,114302,

%U 8192,128,256,32768,854473,5524088,10142461,5524088,854473,32768,256,512,131072

%N T(n,k) = Half the number of n X k binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I.

%C Table starts

%C ...1......2.........4............8............16.............32.............64

%C ...2......8........32..........128...........512...........2048...........8192

%C ...4.....32.......253.........1970.........15109.........114302.........854473

%C ...8....128......1970........28952........407498........5524088.......72544970

%C ..16....512.....15109.......407498......10142461......235950302.....5190742489

%C ..32...2048....114302......5524088.....235950302.....9107867048...323797652462

%C ..64...8192....854473.....72544970....5190742489...323797652462.18095156337973

%C .128..32768...6323090....927723512..109049720858.10764286026008

%C .256.131072..46390429..11603925098.2205335209381

%C .512.524288.337896422.142479782648

%H R. H. Hardin, <a href="/A213418/b213418.txt">Table of n, a(n) for n = 1..96</a>

%H R. P. Anstee, <a href="http://dx.doi.org/10.1016/0097-3165(80)90008-4">Properties of (0,1)-matrices with no triangles</a>, J. Combin. Theory Ser. A 29 (1980), no. 2, 186--198.

%H H. J. Ryser, <a href="http://www.jstor.org/stable/2099147">Combinatorial configurations</a>, SIAM J. Appl. Math. 17 1969 593--602.

%e Some solutions for n=4 k=4

%e ..0..1..1..0....1..0..1..1....0..1..0..0....1..0..1..0....1..0..0..0

%e ..1..1..0..0....1..0..1..0....1..0..1..1....0..0..0..1....0..1..1..0

%e ..0..1..0..0....1..1..0..0....1..0..0..1....1..0..1..0....1..0..1..1

%e ..0..1..1..0....0..1..0..0....1..0..1..1....1..0..1..1....1..1..1..1

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ and _N. J. A. Sloane_, Jun 10 2012

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Last modified September 13 10:14 EDT 2024. Contains 375904 sequences. (Running on oeis4.)