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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column prime, read as a base 3 number with top and left being the most significant digits.
7

%I #4 Sep 11 2015 13:33:35

%S 5,5,5,23,44,23,47,83,83,47,133,784,2802,784,133,369,2632,8086,8086,

%T 2632,369,1206,19665,218493,473294,218493,19665,1206,3427,92550,

%U 716874,1726432,1726432,716874,92550,3427,11146,663483,35791690,170946506

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column prime, read as a base 3 number with top and left being the most significant digits.

%C Table starts

%C .....5......5.......23........47.......133.......369.....1206......3427...11146

%C .....5.....44.......83.......784......2632.....19665....92550....663483.3565229

%C ....23.....83.....2802......8086....218493....716874.35791690.142423172

%C ....47....784.....8086....473294...1726432.170946506

%C ...133...2632...218493...1726432.315759093

%C ...369..19665...716874.170946506

%C ..1206..92550.35791690

%C ..3427.663483

%C .11146

%H R. H. Hardin, <a href="/A262122/b262122.txt">Table of n, a(n) for n = 1..48</a>

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Sep 11 2015