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T(n,k)=Sum of neighbor maps: number of nXk binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 nXk array
6

%I #4 Jan 21 2013 16:28:40

%S 2,2,4,8,12,8,16,64,48,16,24,256,512,256,32,64,992,3772,3772,856,64,

%T 128,4096,31744,63200,32768,4096,128,232,16384,262144,1048576,1048576,

%U 262144,15872,256,512,65344,2097152,16777216,33421056,16777216,2097152,65344

%N T(n,k)=Sum of neighbor maps: number of nXk binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 nXk array

%C Table starts

%C ....2......2........8........16.........24.........64.......128........232

%C ....4.....12.......64.......256........992.......4096.....16384......65344

%C ....8.....48......512......3772......31744.....262144...2097152...16728064

%C ...16....256.....3772.....63200....1048576...16777216.268281856.4294967296

%C ...32....856....32768...1048576...33421056.1073741824

%C ...64...4096...262144..16777216.1073741824

%C ..128..15872..2097152.268281856

%C ..256..65344.16777216

%C ..512.259584

%C .1024

%H R. H. Hardin, <a href="/A221666/b221666.txt">Table of n, a(n) for n = 1..59</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000079

%Y Row 1 is A220172

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 21 2013