%I #4 Feb 24 2014 07:55:56

%S 3,9,9,22,67,22,51,376,376,51,121,1867,4294,1867,121,292,9489,41046,

%T 41046,9489,292,704,50232,405636,721939,405636,50232,704,1691,267174,

%U 4245918,13265123,13265123,4245918,267174,1691,4059,1408341,44773061

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors

%C Table starts

%C ....3.......9.........22............51.............121................292

%C ....9......67........376..........1867............9489..............50232

%C ...22.....376.......4294.........41046..........405636............4245918

%C ...51....1867......41046........721939........13265123..........261676376

%C ..121....9489.....405636......13265123.......459256128........17315827838

%C ..292...50232....4245918.....261676376.....17315827838......1266938409578

%C ..704..267174...44773061....5206684654....658399071392.....93481623913793

%C .1691.1408341..466364332..102053610873..24577532667851...6747651769489946

%C .4059.7395987.4831077908.1987295524193.910817281935043.483084194221969236

%H R. H. Hardin, <a href="/A238323/b238323.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)

%F k=2: [order 13]

%F k=3: [order 43]

%e Some solutions for n=3 k=4

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

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

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

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

%Y Column 1 is A202882(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 24 2014