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T(n,k)=Number of nXk 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.
9

%I #8 Jul 19 2023 09:40:20

%S 1,3,3,9,35,9,22,265,265,22,51,1849,5493,1849,51,121,13345,109119,

%T 109119,13345,121,292,96941,2223723,6092872,2223723,96941,292,704,

%U 701275,45332961,348151747,348151747,45332961,701275,704,1691,5071167,922352267

%N T(n,k)=Number of nXk 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

%H R. H. Hardin, <a href="/A202889/b202889.txt">Table of n, a(n) for n = 1..199</a>

%e Table starts

%e ...1.......3...........9.............22.................51

%e ...3......35.........265...........1849..............13345

%e ...9.....265........5493.........109119............2223723

%e ..22....1849......109119........6092872..........348151747

%e ..51...13345.....2223723......348151747........56006562037

%e .121...96941....45332961....19914296913......9024909392725

%e .292..701275...922352267..1137589582096...1452080571954205

%e .704.5071167.18770352883.64992189188797.233641209300452607

%e Some solutions for n=3 k=3

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 25 2011