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T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its king-move neighbors
6

%I #5 Mar 31 2012 12:35:51

%S 1,1,1,1,3,1,2,5,5,2,3,9,11,9,3,5,19,29,29,19,5,8,37,89,109,89,37,8,

%T 13,71,245,531,531,245,71,13,21,141,669,2276,4194,2276,669,141,21,34,

%U 279,1891,9485,28496,28496,9485,1891,279,34,55,549,5297,41333,189978,304844

%N T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its king-move neighbors

%C Table starts

%C ..1...1.....1......2........3..........5............8.............13

%C ..1...3.....5......9.......19.........37...........71............141

%C ..1...5....11.....29.......89........245..........669...........1891

%C ..2...9....29....109......531.......2276.........9485..........41333

%C ..3..19....89....531.....4194......28496.......189978........1323249

%C ..5..37...245...2276....28496.....304844......3197967.......35028275

%C ..8..71...669...9485...189978....3197967.....52522415......903001960

%C .13.141..1891..41333..1323249...35028275....903001960....24448162531

%C .21.279..5297.179345..9160222..381385173..15450857019...658820676720

%C .34.549.14753.769838.62861079.4118355098.261935376002.17580172417425

%H R. H. Hardin, <a href="/A183386/b183386.txt">Table of n, a(n) for n = 1..180</a>

%e Some solutions for 6X5

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Jan 04 2011