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T(n,k) = number of nXk 0..1 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..1 array.
8

%I #8 Sep 13 2013 21:48:03

%S 2,4,4,8,16,8,16,64,64,16,32,252,512,252,32,64,992,3928,3928,992,64,

%T 128,3900,29808,56472,29808,3900,128,256,15328,224720,796568,796568,

%U 224720,15328,256,512,60228,1690048,11130176,20729216,11130176,1690048,60228

%N T(n,k) = number of nXk 0..1 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..1 array.

%C Table starts

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

%C ...4.....16.......64.........252...........992.............3900

%C ...8.....64......512........3928.........29808...........224720

%C ..16....252.....3928.......56472........796568.........11130176

%C ..32....992....29808......796568......20729216........533254872

%C ..64...3900...224720....11130176.....533254872......25205141664

%C .128..15328..1690048...155031688...13667372880....1186378174632

%C .256..60228.12696384..2156604552..349809115952...55757344229608

%C .512.236624.95336800.29985039328.8948779914072.2619135139987152

%H R. H. Hardin, <a href="/A228986/b228986.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 6*a(n-1) -7*a(n-2) -6*a(n-3) +6*a(n-4)

%F k=3: [order 11]

%F k=4: [order 35] for n>36

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Sep 10 2013