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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 4 of their horizontal and vertical neighbors in a random 0..3 nXk array
5

%I #4 Dec 21 2012 20:03:20

%S 2,2,2,8,16,8,16,48,48,16,24,256,512,256,24,64,928,4096,4096,928,64,

%T 128,4096,30766,62648,30766,4096,128,232,15820,262144,1048576,1048576,

%U 262144,15820,232,512,65536,2097152,16777216,33358976,16777216,2097152,65536

%N T(n,k)=Sum of neighbor maps: number of nXk binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their horizontal and vertical neighbors in a random 0..3 nXk array

%C Table starts

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

%C ....2.....16.......48.......256........928.......4096.......15820......65536

%C ....8.....48......512......4096......30766.....262144.....2097152...16728064

%C ...16....256.....4096.....62648....1048576...16777216...268435456.4294967296

%C ...24....928....30766...1048576...33358976.1073741824.34348186888

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

%C ..128..15820..2097152.268435456

%C ..232..65536.16728064

%C ..512.259584

%C .1024

%H R. H. Hardin, <a href="/A220805/b220805.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A220172

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Dec 21 2012