%I #4 Jan 11 2013 05:34:39

%S 1,3,1,7,17,1,17,119,99,1,41,866,2008,577,1,99,6328,46105,33873,3363,

%T 1,239,46211,1010078,2460824,571358,19601,1,577,337274,22181855,

%U 162430981,131347807,9637322,114243,1,1393,2460918,487335857,10794156688

%N T(n,k)=Number of nXk arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2

%C Table starts

%C .1........3............7................17...................41

%C .1.......17..........119...............866.................6328

%C .1.......99.........2008.............46105..............1010078

%C .1......577........33873...........2460824............162430981

%C .1.....3363.......571358.........131347807..........26135748494

%C .1....19601......9637322........7010554450........4205264399891

%C .1...114243....162555929......374176705928......676612123702617

%C .1...665857...2741882383....19970973695923...108863121975329470

%C .1..3880899..46248186229..1065911268786396.17515379016294357354

%C .1.22619537.780082534460.56890876705125765

%H R. H. Hardin, <a href="/A221328/b221328.txt">Table of n, a(n) for n = 1..96</a>

%e Some solutions for n=3 k=4

%e ..1..2..0..1....2..1..2..0....2..1..0..2....2..1..1..1....2..2..1..2

%e ..1..0..2..1....1..1..0..0....1..1..2..0....0..2..0..1....0..0..0..2

%e ..1..1..2..0....1..2..1..1....1..0..2..0....1..1..0..2....2..0..1..0

%Y Column 2 is A001541

%Y Row 1 is A001333

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Jan 11 2013