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T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors
12

%I #5 Mar 31 2012 12:37:24

%S 1,2,2,4,8,4,8,28,32,8,16,100,196,128,16,32,356,1268,1372,512,32,64,

%T 1268,8128,16084,9604,2048,64,128,4516,52184,185344,204020,67228,8192,

%U 128,256,16084,334948,2142580,4226368,2587924,470596,32768,256,512,57284,2149988

%N T(n,k)=Number of nXk 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors

%C Table starts

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

%C ...2.....8......28.......100.........356..........1268............4516

%C ...4....32.....196......1268........8128.........52184..........334948

%C ...8...128....1372.....16084......185344.......2142580........24754628

%C ..16...512....9604....204020.....4226368......87985748......1830045552

%C ..32..2048...67228...2587924....96373248....3613193828....135288700496

%C ..64..8192..470596..32826932..2197585152..148378294612..10001404535216

%C .128.32768.3294172.416398420.50111214592.6093257064980.739367693888784

%H R. H. Hardin, <a href="/A208709/b208709.txt">Table of n, a(n) for n = 1..631</a>

%e Some solutions for n=4 k=3

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

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

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

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

%Y Column 2 is A004171(n-1)

%Y Row 2 is A104934

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Mar 01 2012