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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the determinants of 2X2 subblocks nondecreasing rightwards and downwards
9

%I #5 Mar 31 2012 12:37:04

%S 256,2338,2338,15040,27611,15040,84899,275853,275853,84899,456043,

%T 3684581,7148335,3684581,456043,2470216,56088455,198539736,198539736,

%U 56088455,2470216,13615376,888172440,5296848762,11646996582,5296848762

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the determinants of 2X2 subblocks nondecreasing rightwards and downwards

%C Table starts

%C ......256.........2338..........15040..............84899................456043

%C .....2338........27611.........275853............3684581..............56088455

%C ....15040.......275853........7148335..........198539736............5296848762

%C ....84899......3684581......198539736........11646996582..........674941613200

%C ...456043.....56088455.....5296848762.......674941613200........69845358912381

%C ..2470216....888172440...139786868632.....42501311863619......8486771114466915

%C .13615376..14267356381..3650380799573...2691721552273415....932371404894182926

%C .76027865.230651852383.95296479247095.175740162358914695.109561074506695905962

%H R. H. Hardin, <a href="/A205027/b205027.txt">Table of n, a(n) for n = 1..127</a>

%e Some solutions for n=4 k=3

%e ..3..1..0..0....1..2..3..3....0..3..0..3....3..3..1..3....3..2..0..3

%e ..1..0..0..1....2..2..2..2....1..2..0..3....3..1..0..0....2..0..0..1

%e ..2..0..0..2....0..0..0..0....1..0..0..1....3..0..0..3....2..0..0..1

%e ..1..0..0..2....3..0..2..2....2..0..0..3....3..0..0..1....1..0..0..2

%e ..1..0..0..2....2..0..3..3....0..0..0..1....0..0..0..3....0..0..0..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 21 2012