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T(n,k)=Hilltop maps: number of nXk binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, vertical or antidiagonal neighbor in a random 0..3 nXk array
8

%I #4 Oct 27 2012 06:07:10

%S 1,3,3,7,15,7,15,63,63,15,29,253,509,253,29,57,1009,4081,4081,1009,57,

%T 113,4033,32641,65409,32641,4033,113,225,16129,261121,1046529,1046529,

%U 261121,16129,225,449,64511,2088955,16744435,33488029,16744435,2088955

%N T(n,k)=Hilltop maps: number of nXk binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, vertical or antidiagonal neighbor in a random 0..3 nXk array

%C Table starts

%C ....1........3...........7..............15................29

%C ....3.......15..........63.............253..............1009

%C ....7.......63.........509............4081.............32641

%C ...15......253........4081...........65409...........1046529

%C ...29.....1009.......32641.........1046529..........33488029

%C ...57.....4033......261121........16744435........1071613317

%C ..113....16129.....2088955.......267910753.......34291593409

%C ..225....64511....16711551......4286570153.....1097330469185

%C ..449...258015...133691649.....68585092161....35114559214497

%C ..895..1031935..1069527065...1097360991969..1123665390953149

%C .1783..4127233..8556167553..17557768153359.35957276389513409

%C .3551.16506913.68448948737.280924166963785

%H R. H. Hardin, <a href="/A218372/b218372.txt">Table of n, a(n) for n = 1..127</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A218189

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Oct 27 2012