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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum of every 2X2 subblock equal
9

%I #4 Feb 02 2014 12:25:06

%S 81,563,563,4042,11205,4042,30045,221994,221994,30045,225731,4552617,

%T 11703666,4552617,225731,1709398,93224611,638436002,638436002,

%U 93224611,1709398,12985257,1918085364,34552648978,93104881597,34552648978

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum of every 2X2 subblock equal

%C Table starts

%C .......81.........563............4042..............30045................225731

%C ......563.......11205..........221994............4552617..............93224611

%C .....4042......221994........11703666..........638436002...........34552648978

%C ....30045.....4552617.......638436002........93104881597........13403891066319

%C ...225731....93224611.....34552648978.....13403891066319......5114994760537075

%C ..1709398..1918085364...1877852845426...1939706609440732...1964124791456164266

%C .12985257.39451935691.101931021677874.280172591227575985.752460086062505325739

%H R. H. Hardin, <a href="/A237035/b237035.txt">Table of n, a(n) for n = 1..544</a>

%F Empirical for column k:

%F k=1: a(n) = 9*a(n-1) -83*a(n-3) +15*a(n-4) +60*a(n-5)

%F k=2: [order 7]

%F k=3: [order 9]

%F k=4: [order 15]

%F k=5: [order 23]

%F k=6: [order 37]

%F k=7: [order 59]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 02 2014